Traveller does have a workable character advancement.
The experience rules cover gaining better skills or increasing your abilities, however, this is expressed in years of training, which initially puts players off.
But if you are running continuous adventures with the same character, then space travel becomes a vital component, it always takes at least a week to go anywhere, and you'll always have about a week in a star system, over the course of the campaign these weeks add up to months and then years, so if you assume your character spends most of their time shipboard doing training, that is where the advancement comes from.
As the characters move from adventure to adventure they will travel, moving from one end of a sector to another could easily take a few months, and even some adventures cover months of space travel, it all starts to add up.
A financial limit could be placed on this as well, character would have to continuously make money to pay for it all, just travelling wont be enough, they'll have to earn a living, normally by crewing or by trading.
The blocker on all this is age, but that's the decision you make on character creation, having an older character with more skills is going to cause problems later, something you need to think about if the character is intended to be played again.
If you are running one-shot adventures then this doesn't really apply, but it wont apply in D&D either.