For karate, important uses of the gluteus muscles include:
explosively closing distance, particularly when the back leg is bent and the knee
is turned forward, so you can think of the back leg contributing
something akin to a sprinter pushing over the starting block,
delivering a strong, explosive jab or reverse punch (the glutes will
tend to contract on ...
It's quite easy.
Go to the open training time, be early.
Ask the trainer, sifu etc., if you may join.
They will ask back if you have some experience.
Tell them what is. They should know. Just don't brag.
As a sign of respect, take a white belt to the training.
They may offer you to wear your old black belt as a sign of respect.
Stick to white.