I got to thinking about exactly what sorts of auxiliaries a Traveller navy would need. Here's a list to start with. I broke it down into a few basic categories:
Logistics Ships
* Tankers: obviously, needed to exted the range of fleets without frontier refuelling
* Ammunition Ships: mostly to resupply missiles, which some units will use in large numbers.
* Stores Ships: food, other stores, and spare parts.
Stores are likely to be much smaller in volume than either fuel or ammo. Thus, stores might be carried on tankers or ammo ships, rather than on dedicated stores ships.
Support Ships
* Repair Tenders: large dispersed structure ships that serve as mobile docks and repair yards
* Tugs/Salvage Ships: high-thrust ships capable of pushing or pulling disabled major warships. Some might use jump nets (see Supp 9) to carry smaller ships or other cargoes through jump space.
* Hospital Ships: Self-explanatory. Need lots of small craft to collect casualties, plus dock to land additional small craft.
Transports
* Drop Assault Ship: for landing marines by drop capsule, must be very fast to minimize warning time. Possibly with jump capability like the J-5 fleet intruders.
* Heavy Lift Ship: large dispersed structure ships carrying large and odd sized cargoes (may be similar to repair tenders)
* Assault Transport: carries Army/Marine armored formations, with landing craft to land troops.
Merchant ships taken up from trade also carry troops and equipment.
Miscellaneous
* Fleet Courier: Small, long-range (there is already a canonical design).
*Intelligence Collector: Covert deep-space vesels, possibly carrying small jump ships to send reports.
*Training ships: probably old warships (light cruisers seem promising) with extra berthing and training spaces replacing some bay armament.
* Command Ships: squadrons and fleets are typically commanded from modified combatants, but high-level (e.g. Sector/Domain) command may require dedicated command ships to ensure the commander and staff can move when needed (though commuications dicatates that they not move often, or do so on a pre-planned schedule). Defensive armament, but large carried craft capacity, including many couriers.
Note that a lot of the types found in modern navies didn't seem appopriate. Survey and research functions fall to the Scouts.