If a catholic who is already a priest marries, he can no longer serve as a priest except to hear a confession if a person is in danger of dying. I don't think they are permitted to say mass privately, although some do. I don't think any catholic who is married can be accepted in the seminary. This has been discussed at length on the internet.
A catholic can transfer to a rite that allows married priests. Ministers and priests from other churches who convert can be priests, (Anglican, etc.), but if their spouse dies, they are not allowed to remarry and continue in the priestly ministry.