Currently, the last entry on the series is Rhythm Tengoku: The Best+ (Rhythm Heaven Megamix) released in 2015 fot the 3DS. However, the producer has expressed interest in developing a new game for the Switch. You can read more about it here.

Will we get a new game (or remake, as long as it's a new release and not part of, say, nintendo online) of the series for Switch?

Resolves to NO whenever Nintendo announces they won't make more games for Switch or 1 year passes after their last release for it (in case they don't announce it officially).