The Brensholmen ferry terminal is a popular spot for travelers looking to hop over to Senja Island from Tromsø, but be warned—you can't make reservations, the the ferry can only accommodate about 20-30 cars at a time, depending on how many camper vans are in line (since the camper vans take up more space).
You'll want to arrive as early as possible, and just plan for the fact that you won't make it on the initial ferry you'd like to. If you do—great!—but be prepared not to.
The crossing time between here and Botnhamn, on Senja, is about 45 minutes, one-way, and the ferry actually operates year round, with more crossings in summer than winter.
The summer schedule usually starts around mid-April and lasts through mid-September. Be sure to double check the local timetables for seasonal sailing dates.