OK, some general thoughts about character progression and experience.
(This is basically similar to how I handle all my old Traveller games with characters, actually with most RPG's cause I have never liked, poof you gain a level and get new skills, magic, stats, etc.)
I don't believe that once you complete character generation (Traveller) that the character stops learning.
I also don't believe in Power Munchin.
So, with that in mind here is the basic way to grow (advance in games)
First, the character must be doing something over the course of time, like a job, dedicated hobby, school, etc. For Traveller, that is a period of one year.
Second, the character (player) must declare what skills (or knowledge) that they are trying to learn, improve or devote time to.
Third, over the course of play and in that one year, the character must have devoted time and effort toward that skill (or knowledge).
Then depending on play and how much time was spent over the year, the player either gains a new skill at level 0 (zero) or 1.
Or may increase a known skill by 1 level.
Or the player may roll versus appropriate stat to determine increase (depends on amount of time and current skill level).
More than one skill can be done this way during a year. Each additional skill (or knowledge) attempted during the same year adds the following modifiers
Primary skill declared +2 difficulty
Secondary skill declared +4 difficulty
Third plus skill declared +6 AND +2 to each skill roll for each skill attempted
Ie, 3 skills attempted in 1 year, Primary skill is now a +4 difficulty, secondary +6, third skill +8
Ie, 4 skills attempted in 1 year, Primary skill is now a +6 difficulty, secondary +8, third skill +10, fourth skill attempted +10
I usually have the player roll under their stat including modifiers
For example:
In a nutshell, it is easier for a character that has Nav skill, who also is the primary Navigator for a ship over the course of the year, actively applies their skill (ie makes some rolls) and/or does something above normal with that skill (helping a mission achieve greater success, plotting all courses to compare them to the computer, attempts to teach or teaches the skill to someone, etc) They will probably gain one level in Nav skill (this assuming that they already have the Skill Navigation (Nav)
If the same character only does what is needed as the Nav, using their Nav skill only when required, they will probably get to roll for the possibility of a skill increase with their current Nav skill as a negative modifier (and/or possibly other modifiers). (Ie it is hard to learn something new when you already know so much about it)
Another example:
A character decides to take up a hobby (or continue a hobby) and they actively, daily use or employ that hobby they will probably get a roll versus the appropriate stat with either positive or negative modifiers to determine if they get to increase that hobby skill. Most hobby skills are either no level or level 0 and some are level 1. If a hobby skill becomes level 2 they are no longer considered a hobby and are treated like an ordinary skill.
A character that only occasionaly uses a hobby skill, will get a negative modifier to a stat roll if they attempt to increase the said skill.
(Note: you can replace the word hobby with a level 0 skill if the player wishes to actively learn a new skill that they don't have.)
Another example:
CrossTraining, if required due to job requirements (like most small ships require crew to learn or be knowledgable in at least one other ship skill), time and effort can be used to learn a new skill.
The character again must actively take part (OJT, On the Job Training) regularly to learn make a roll for that new skill.
Another example:
School, Basically use the school/college text out of the book. Kind of boring to RPG but it is possible. It is also possible to do just what the book requires if you are wanting to advance that character some in the middle of play. They go to school, the world and the other characters carry on, maybe to met again later.
So, as a rehash;
A character (player) must declare what skill(s) wanting to learn/increase.
The character must actively spend game time doing or attempting to do (or learn about) that declared skill (knowledge).
After some time (usually a years period or a college year) the character can attempt to prove/show that they have improved or learned something new (ie make a roll for it).
Dave Chase