If you are carrying a "simple" Papilloma virus infection (even high-risk viruses or potentially oncogenic ones) or if you carry a virus-induced lesion such as a CIN (cervical dysplasia), it is not usually necessary to use condoms, because you are already infected with the virus and the use of condoms does not change the natural course of the virus.
Basically, carrying HPV (simple) does not alter anything regarding your future nor that of your partner (except in case of exophytic lesions (see below). In principle there is no risk of virus retransmission once you are healed. However, if you smoke, it is strongly recommended that you cease tobacco consumption, as tobacco, even if doesn’t cause the infection, decreases the immune system defenses and favors the persistence of all types of Papilloma virus.