Usage patterns
〈人〉とパートナーを組むto team up with someone as a partner
I teamed up with her as my partner and entered the contest.
〈人〉のパートナーになるto become someone's partner
He became my business partner.
パートナーを探すto look for a partner
She is looking for a life partner through a matchmaking service.
パートナーがいるto have a partner (spouse or significant other)
He already has a long-term partner.