Tybalt is Juliet's cousin, originally, Tybalt wanted to duel Romeo instead. But since he and Juliet are married, he cannot fight Tybalt as he is basically his cousin-in-law, thus, Romeo rejects Tybalt's challenge. Mercutio finds this quite cowardly as a result he himself challenges Tybalt to fight.
The answer is action verb because strive is something that someone can do.
I would go with dominion, which means a position of authority.
At her (position of authority) as chancellor of the university...
