You ask a very complicated question that might best be answered by a doctor or a physical therapist. The severity and location of the tear, your physical health, and your body’s typical healing cycle / time will all affect what works and what doesn’t.
The direction of your movement might also be altered for a while. I’ve never had a client actively training with me with a torn labrum, but my neighbor just had surgery to repair her tear. She was on a mobility machine for 2 weeks, crutches for 2 weeks, and she is supposed to only move forward (no twisting, no side-stepping) for another couple of months. But for her, the surgery now means avoiding a hip replacement later.
If you’ve been to the doctor to find out that you have this condition, ask for a referral to a physiscal therapist.