marine or ice
You might have fantastic fishing in the sea just outside Tromso. Large halibut and the Barents cod coming down towards the Lofoten to spawn. Many guides in Tromso should be able to take you out. The regular tourist webpages of Tromso should be able to connect you with a fishing guide.
If you travel inland for some hours (southeast of Tromsø), there is the chance of ice fishing for large Arctic charr in the national parks (Dividalen and Altevann areas), but you will need a very very long day to be able to get something out of that.
No spey/salmon fishing in the Troms region until late June, I would say.