No your husband/partner does not need to be tested. HPV is very common, and we do not know how long you may have had it. Your partner is also likely to have had HPV, and they may still have it, or their body may have dealt with it.
It usually causes no symptoms and we do not test for it in men. If you are in a same-sex relationship, then we would always advise that your partner/wife attend for cervical screening (a smear test) when they are due