It's not so easy, as the original verb form is obscure Latin and not used in English. You would "be penitent", "show penitence", "make an act of penitence" or "do something as an act of penitence". The closest verb form would be be "to repent".

A person can repent and ask to be forgiven. You can repeat gossip, but it makes no sense to peat it.

Penitent is not a verb, but a noun and an adjective.