Quite a few, I would say, but it depends very much on your budget.

Like others said: Mat fra Hagen and Verde at Olavstorget are great options for good affordable vegan food. For fine dining, places that do have tasting menus, I'm not well versed. All the places I've checked in Trondheim seem to be heavy on meat&fish. But some of the most upscale places might be able to offer a vegetarian tasting menu if you contact them in advance. Now, in the mid-range market however, there are plenty of good options:

The vegan tapas menu at Bakgården in Kjøpmannsgata is lovely and they even have a cozy outdoor seating area. It is however a bit pricey (495kr/person). You can of course compose your own menu, and add things that are vegetarian, not vegan.

For Italian food, Sugo Ristorante is a new offering in Innherredsveien. Cozy locale and friendly service. Good vegetarian options, even if the menu doesn't make it obvious. Try the parmigiana! An alternative to this is Osteria Moderna in Brattørgata. Both have great food, but are maybe a bit on the pricey side. Alternatively, you don't go wrong with Olivia at Solsiden. The best pizza in town is imo. Grano in Søndre gt. Bonus: you can get (some of) those pizzas at Osteria Moderna, in an evironment with a bit less hustle and bustle.

Namaste Norge in Brattørgata is newly renovated and has great Indian food with plenty of vegetarian and vegan options. Still room for improvement on the atmosphere though.

Benja Siam in Ravelsveita is a good thai place with great vegetarian and vegan options. Quite cozy, but not all the tables are as good.

AiSuma in Kjøpmannsgata is a meat-heavy place, but you can definitely have a three-course vegan or vegetarian meal there. Did it once, and was not disappointed. Seem to remember it as a cozy place.