The canon Traveller Imperium is vast.
Generally people set their campaigns in a corner of the 3I and forget the rest however another option is to set a campaign specifically around a long journey.
Core to Rim (or vice versa)
An epic journey between Core and Rim lasting years. Some possible back stories for this are
1. A new Baron has been ennobled and given a new fiefdom on the rim and needs escorting there.
2. A player in the core might get an inheritance on a remote planet on the rim.
3. A patron has a treasure map of some kind where the treasure is on a very distant planet.
4. Inside the Imperium the Imperial Scout Service are used as a secret service and Scout personnel with a ship get missions to check out what’s going on on remote planets off the main trade routes.
The Scout Service has the job of maintaining hazard navigation satellites in backwoods systems.
Mission is to take a 200 dton maintenance ship on a four year contract (average c. month per system) along the J1 spinward main (as in Twilight’s Peak) checking on all the satellites.
Ship has small crew and large service bay so satellites can be physically retrieved and worked on if necessary.
(In my case two Scout players: pilot and engineer and a medical droid.)
Then conjure up a random number of episodic adventures along the way.
(could add Twilight’s Peak stuff if have that adventure)
Where’s My Ship?
Player musters out at a sub-sector capital with a ship’s deed but there’s been a mixup – the ship registered to them is waiting at an adjacent sub-sector capital.