We do know, from the mish-mash of materials, that you have the regular Imperial fleets that are assigned to entire sectors, like the Marches, and these are typically top of the line units. Sub-sector fleets can be a mix of latest and greatest to older but still serviceable designs. Then we have units at the local system level, and these can be modern to outdated. Typically even an out-dated warship will triumph over even armed merchants.
Systems need not have their own shipyards, or the necessary TL to purchase, operate, or even maintain their system defense forces. Though I can see that a LOT of just how modern or large these forces are going to be will depend upon the importance of the system and it's ability to pay for it. TL-12 escorts and destroyers would be considered "capital" ships for 3rd tier systems. Maintenance can be done locally using imported materials, and annual and/or heavy maintenance could be done out-system (or even by an engineering ship that comes to do the work).
We've seen, historically, that nations that could not build warships locally going to other nations to buy surplus vessels, or, in some cases, paying for 1st line modern warships (this was especially prevalent leading up to WW1). Local yards may only be able to build smaller hulls, but that does not prevent a world from purchasing and operating modern units. We've seen this mentioned canonically as well with examples of TL-15 SDBs being mentioned as deployed in some systems (and TL-15 is on the very high end of the Imperium).