I vaguely remember something like this (not sure if it was removed or I'm thinking of DS) but I would like to see a "new round" notification shown during tournaments.
Step up to the Arena - Your next opponent awaits! Fight for the chance to earn the (Name of the prize animal)!
Just an example. Not hard to be implemented. Please consider it S8.
P.S. The question marks at the beginning and end of my example were trophy emojis - they disappeared