I give my players a free second specialization at character creation and our wookie hired gun decided to take entertainer and be a professional gladiator, an idea I found awesome and wanted to roll with. our party is as follows:

Wookie Hired gun: heavy, entertained

Human Smuggler: scoundrel, gunslinger

Mirialan Engineer: mechanic, pilot (works for the rebels as an underground contact)

Faleen Smuggler: gambler, force sensitive exile (the player has hilariously bad rolls,one time racking up 12 NAT 1's in a single D&D session, so this seemed appropriate)

???? Colonist: doctor, scout

Incorporating other players into adventures and jobs focusing on the wookie is proving difficult and while we haven't started yet i'm trying to set up some rough plots and adventures for them. So far I plan on having an adventure that requires the wookies to fight in an arena, the gambler to place bets and work the bookies, the scoundrel to get people to bet against the wookie causing their enemies to lose credits (and drive up the wookie's odds? I am researching gambling to see if that is a thing), I plan on having the mechanic work the arena, breaking traps and upgrading others so the wookie has an advantage, and the doctor to heal him between fights while analyzing other opponents for weakpoints.

Beyond that initial adventure i'm not sure ho to incorporate his performance combat and professional gladiator status in a way that allows everyone to participate in the job/adventure and was hoping to get some ideas from you fine folks.

One player can easily work as a manager of sorts. With the kind of scam the Smugglers are playing, there would be an easy way to introduce a recurring antagonist or nemesis. After the first show, the players could easily get hired for a showing that's a trap set by some rivals, or a Hutt wants the Wookiee as a 'permanent employee'. If the Engineer is a Rebel agent, then they could use the opportunity to pick up some supplies to smuggle to a Rebel cell (depending on if the rest of the group knows about their sympathies, it could be 'no, don't worry, this is just some stuff for a friend, I promise' or 'listen, this is really important for the war effort, I'd really appreciate it'). The Colonist is tricky, but combine Doctor and Scout, and you have a character who might be willing to venture into the jungle to find a rare plant for some medicine. That could be worked in somehow.

What works best is do a session and have everyone discuss what they want and how they know each other. It may take some time but you should be able to hammer out a framework.

I have plenty of plans for focusing on the others. My main concern is integrating the other characters into a job or storyline that puts the wookie in the spotlight.

What obligations have the PC's got?

Within this setup things are straight forward, one thing that would shake the rules up is a tournament of some description. A hutt hears of this wookies exploits and sends him a invite to a hutt party, little does he know that it's really a glorified gladiatorial Olympics, with everything from ship racing, gambling and other bonkers nuts. Of course the Hutt requests (and anyone with any underworld knowledge knows that a "request" is a formal order. If you don't, terrible things start to happen.) that he bring's along attendants, Obligatons and such work for his.

Musicians that Jabba likes are invited for a single performance. If he likes them enough, then they just don't get to leave.I wonder if they start singing Hotel Tatooine after this...?

Invite the Wookiee (and company) to a Hutt gladitorial spectacle, let him do what he does best, maybe shoving some other players in against their will... Then when the Hutt is good and pleased and feeling generous, he makes them an offer that they can't resist. A lifetime contract, so to speak...