To Keep A Pet, To Raise A Pet, To Own A Pet
transitive verb, godan verb
The kanji is domesticate. When you domesticate an animal, you get to keep a pet of some kind. You'd use this to describe when you are keeping a dog or cat or something.
かう
The reading is the one you learned with the kanji. The か of cat!
何か爬虫類をペットに飼いたいな。
I want to keep some reptiles as pets.