So how do these characters improve over time? Here's what the game itself says on the matter:
The experience which is gained as the individual character travels and adventures is, in a very real sense, an increased ability to play the role which he has assumed.What that means is that characters don't improve in Traveller but players do. How old school is that? To be fair, there are rules for taking courses, including by correspondence, to slowly improve one's skills, but this avenue takes years of game time, costs money, and isn't guaranteed. As in real life, it's quite possible to take a course and come away with no meaningful benefit for one's efforts.
What's funny is that, as a younger guy playing Traveller, we never even noticed the lack of experience rules. I can tell you for a fact that not a single one of my players ever asked to have his character attend the local technical university to improve his Computer or Electronic skills. Even though level advancement was deeply ingrained in us through regular play of D&D (and, to a lesser extent, Gamma World, whose advancement system is a bit peculiar), we just took it as given that characters who were in the mid-40s probably didn't get much "better" over time, although they did become richer, more influential, and more knowledgeable about the universe around them -- and we were OK with that.
Makes me wonder what RPGs might have been like if OD&D had been built on similar presumptions about experience and learning as Traveller ...