Basically, what you are talking about is Player Motivation, not Character Motivation.
That's basically it. Traveller characters are motivated by the things that motivate
people. Respect, avarice, altruism, love, hate, fear, pride, loyalty, betrayal, revenge... that sort of thing. The LBBs didn't have rules for that, outside of material possessions and the slow potential for some skill development. There's still not much in newer versions of the rules.
There isn't an out-of-universe points system that feeds back into abilities, self-esteem, and external validation. For the characters, it's probably not necessary -- in the real world, people are motivated by a lot of things.
Players might want something external for bragging rights, but that's limited by different referee/universe conceptions of value (in archaic terms, "monty haul" vs "killer DM" campaigns). The archetypal campaign puts a few PCs in a Free Trader to start with, with the hope of upgrading to a Subsidized Merchant or Far Trader at some point perhaps. I started my Play-by-Post with the PCs in possession of a (well,
the) 600Td Collector-Drive starship and before they really get going here they're now flying a Type T Patrol Cruiser. Does this make the characters "higher level" than the archetypical party because they get points for having a valuable starship? Not really -- it just changes the situations they face and what resources they have available.
Characters roll into play having already completed their level-grinding. They continue on based on whatever the players see as the character's motives, and if their goal turns out to not be all that in the end (owning your own moon can be boring!) they can retire so their respective players can seek new challenges with new characters.
This puts a lot of additional work onto the referee
and the players. The players have to develop their characters' motivation (simple avarice works, but doesn't provide a lot of depth), and the referee has to create a setting with allies who the players can develop attachments to, adversaries worthy of enimity, and a society that the PCs can either find a place within, rebel against, or simply escape.
Experience points and levels are a cop-out.
