So if I have genital warts and get them removed is there still the possibility of giving them to my partner? Will I always be contagious or does it eventually go away when the body suppresses it to undetectable amounts?

I was diagnosed with low-grade cervical dysplasia a while ago and following my most recent test I was told that I no longer had the dysplasia but the high-risk hpv that caused it was still there… Does this mean that cervical dysplasia could come back? And is it possible that the hpv could ever go away?