Please be aware that Pirates of Drinax is not perfectly written; there are holes and such which you will need to fill. Prep takes more work than just a single read-through; and you might want to adjust several things -- the deadliness (and/or sneakiness) of the Harrier, when the Players first get it, how much loot is available & worth, how prevalent psionics are, how 'Standing' (and the completely worthless 'Letter of Marque') works, and so on. No two referees will fix things the same way.
Somewhere around here I have a list of collected tips....
[Edit:] Here are a few suggestions for your consideration (sorry for the long post):
1} Do not start the PoD campaign with the PoD campaign -- let them do some minor missions (and maybe encounter the reputation of Margaret Blaine, infamous pirate) somewhere in the Reach (maybe run 'Exodus', with the Grehai Movement as a minor adversary), and plan to have them have a few amiable encounters with pirates -- maybe 'off duty', or celebrating, or something. Set the stage; establish important elements from the campaign early:
a} The Aslan are the big scary, enemy;
b} everybody hates (but still buys stuff from) the conniving & exploitative GeDeCo,
c} people still tell wistful stories about the 'glory days of the Sindalian Empire',
d} sometimes good folks are forced into piracy to make ends meet, or by other circumstances,
e} the Grehai movement is a recent development, and seems to be a good thing,
f} the Third Imperium is remote, and not interested in getting involved in solving local problems, etc. ('Fire on the Sindalian Main' could feed into this).
The players happen to end up at Drinax at some point in the story, seemingly organically. At this point Oleb or Rao would notice them, but not trust them (off-world traders are curiosities; the Royal Court will fete them just to get fresh gossip) -- then have them undertake a minor mission or two on behalf of Drinax (not necessarily the Royal Family). Once they have proven to be reliable, start them on the PoD main campaign -- maybe through 'First Prize'.
There are resources out there for a series of mini-adventures to recruit some (or all) of the Vespexer Tribes; in my head-canon their point of contact for this is Prince Harrick. The players may initially come to Rao's attention by working (and succeeding) on these mini-missions.
2} Do not give them the Harrier straight away. Maybe they can struggle to get a ship in the lead-up adventures before they get to PoD -- until then they are buying (or working) passage. Once they are enlisted, have them trying piracy missions in a rattletrap junker; rewards along the way can be better access to cheap repairs at Drinax or similar. Upgrading and restoring the ramshackle 'Class A in name only' royal port of Drinax might form several off-the-cuff filler adventures. Give them the Harrier as a reward for doing a mission ('Treasure of Sindal' is the easy, obvious one if you run it early; otherwise some variant of 'High & Dry' might work, to get the wreck back up to orbit where a Jump-Tug can tow it to Drinax).
Also, the Harrier was given statistics in 1e. In 2e the mechanics of the game changed, and now the Harrier is amazingly, absurdly, game-breakingly different. Maybe consider making the Turret a Particle Beam / Laser / Sandcaster turret, and the Barbette is a Torpedo barbette. Since torpedoes are expensive & hard to find, this makes the barbette more situational -- and ALSO gives the Harrier the ability to use the weapons from 'Treasure of Sindal'. It might also benefit from 'Adjustable Hull' (High Guard Update 2022, page 43) instead of the (expensive, power-hungry, and useless) 'Holographic Hull' that it is listed as having.
3} Remember the timeline -- by 1107 the Fifth Frontier War starts, pulling Imperial Navy assets toward the Spinward Marches (and away from the Trojan Reach); and in 1116, Emperor Strephon is assassinated, the Imperium is in tatters, and the Trojan Reach consumed by the Aslan -- they take Tobia in 1118, and all the worlds up to Gazulin before they are stalled. If you want the Kingdom of Drinax to survive at all, start the campaign well before the suggested 1105 date. I sort of favor starting in ~1094, about 2 years after the explosion at Vorito highport, with 'Vorito Gambit' playing out in 1099, and Finale during or before 1100. I am considering using the 2300 AD third party 'colony development' stuff, and this gives the 'Kingdom of Drinax' a few years to build.
4} If your players are coming from heroic-fantasy, it might be good to do a 'Session minus 1' as well as a 'Session Zero'. The point is to walk through character generation a few times until it is easy, and then (crucially) run a bunch of disposable mook characters through a half dozen 'Snapshot' or 'Azhanti High Lightning' scenarios -- the point being that you need to hammer home the blood-drenched nature of Traveller combat so that they respect violence as a last resort. The goal is for the players to realize that their super-duper-kill-anything starting characters will, with excellent die rolls, usually die in round two instead of round one. If everyone is having fun, maybe do the same with some ship-to-ship combat.
Also, having a stable of a few dozen extra 'Traveller' PCs will be a neat resource; later in the campaign the players are overseeing groups of allies, assets, and factions -- and probably a whole pirate fleet. The 'extra' travellers can be colorful & relatable additions.
5} Do not feel like you are obligated to run the adventures in the PoD campaign in order, or without breaks. Plan carefully how you want the plot to progress, and run the adventures in the order that best supports your plot-line (or what your plot-line ends up being after the players do something crazy and unexpected). Some groups entirely skip 'Treasure Ship', for example. 'Demons Eye' and 'Prodigal Outcast' both take the characters quite far afield. You might want to add your own twists to the adventures, too -- will the players be able to parlay GeDeCo support into taking over some (or all) of the GeDeCo assets in the Reach during the 'Vorito Gambit'? Will players be able to manipulate the outcome of 'Shadows of Sindal' to put Drinax in charge of the Dustbelt? During 'The Knife Edge', can the players talk one or more minor Aslan clans (or maybe even the Ahraoy'if?!) into declaring fealty to Drinax?
6} Try to have one or several characters have ties to Drinax; maybe they aspired to the Star Guard once upon a time, or were a Vespexer from a tribe friendly to the Floating Palace. It is possible to do this on-the-fly during play, by using 'contacts' or 'allies' from Character Generation; but it is probably better to have at least one or two characters start with Drinax or Asim as a home planet. There are careers in PoD book 2 that work.
7} Decide early about the role you want psionics to play in your game. Some GMs run psi-free games because some of the powers might derail or otherwise ruin some adventures; but PoD specifically DOES feature encounters with several psions. Do you want all your players to start with psionics as an option? Is there one player you can trust to not break the game, and role-play correctly, if allowed psionics? Do you want psi-training as something to reward the players later?
8} Be prepared to give the characters truly ridiculous amounts of money. The task of restoring the Kingdom of Drinax is staggeringly huge in scope -- just detoxing Drinax will probably run ten to thirty years, with maybe a dozen TeraCredits spent per year. Double (or more) the money to reduce the time down to a minimum of half of that -- and the characters should probably not expect to see the end of the project. A new starport (including a suitable highport & shipyard) to get Drinax back to an 'A' rating is probably hundreds of GigaCredits, and a similarly long timeline. Rebuilding the agricultural, mining, smelting, manufacturing, and transportation capacity is also hundreds of GigaCredits per year -- and this is just for Drinax; other worlds will need similar investments. All these investments are pointless without people to do the work -- and that means recruiting, vetting, training, transporting & supplying many millions of colonists.
Building empires is so expensive it is not really useful to even think of it in terms of 'Credits'; the sums are too vast. Hook your players on building bases, fleets, starports, networks of agents, universities, housing, factories, terraforming installations, orbital rings, space-based defenses, research think-tanks, and so on -- and soak them for unspeakable sums of cash to build, use, maintain, expand, and repair these assets. But do not be stingy handing that cash out; they should have the money to start some grand (years or decades long) projects, along with monthly or seasonal progress reports to make them feel invested and proud... only to have situations where they do not have the cash to do everything they want. Some things will need to be postponed; scrapped; or put on hold to address some other urgent need that also requires grand expenditures. The rats are still struggling to keep up with the treadmill -- but the treadmill is bigger.
9} GeDeCo & the Third Imperium backing Theev makes very little sense. If you are also running 'Shadows of Sindal' with 'Prince' Richter Grehai, then maybe you want to alter the deal a little. In this version, Richter stumbled across a cache of ancient Sindalian treasure on Theev: A few ships; supplies for a couple small infantry units; a small, hidden (underground!) shipyard; and the blueprints & technology to produce a limited number of types of combat clones -- Blacksand Widows. Theev as a 'Legendary Pirate Haven' is recent, within the last decade or so as Richter built up his power & connections. He has the Pirate Lords on a leash, and collects a small part of their take in exchange for stuff built in the shipyard, and some protection via the Widows. On the other hand, the players may get Theev to declare fealty before Finale -- if they get it to 'Haven' and then defeat or otherwise remove Grehai.
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Iron Spine and the Tktk Convergence can add some episodes to a PoD campaign, too, and give an entry point into Glorious Empire interactions
