I suspect St. Thomas will want to schedule the U in certain sports sooner rather than later.
Hockey is going to make the most sense. The Tommies have already been admitted to the WCHA on the women's side, so the Gophers will play them at least four times a year starting in 2021-22. Men's hockey will likely see each other in a relatively short space of time as well.
Possibly basketball as well, although I don't think the games would be competitive. Softball and baseball would definitely be in play.
Volleyball won't schedule them unless it's in a tournament and football won't play them for a long time imo. Reason being? Volleyball is already a top sport nationally and playing against St. Thomas does nothing for them in terms of seeding for NCAA Tournament purposes. And as for football, St. Thomas is entering the Pioneer League, which doesn't grant scholarships despite being classified as FCS, so it wouldn't be competitive.
Whether it all stays this way for the long term nobody probably knows, but the sports I would look for in terms of possibly immediate scheduling would be hockey, basketball, baseball and softball. Possibly soccer as well.