Unfortunately, Traveller does not really have clear provision for increasing skill levels in the game without devoting large amounts of time to study, when in theory, the player character is not going on adventures. There is some provision in Space: 1889, sort of a Victorian equivalent of Traveller for that. D&D has clear requirements for increased skill levels, but those are pretty much what I think of as "ticket punching".
I view it as if a skill is used successfully during an adventure, where some die-rolling is required to determine success, then a chance exists for skill advancement. Weapons and navigation skills, along with computer skills have the best chance of increase, while skills like Medical have a lower chance. However, if successful use of the Medical Skill is combined with some money and time devoted to study, then that skill level can be increased.
Again, that is just my thoughts, and what the chances are would depend fairly heavily on the skill used.