Thank you for your question. One of the most important strategies to combat most vices is to be aware of instances when you feel or act in an arrogant manner and to stop yourself from doing those things and to talk yourself out of your feelings of arrogance. It is then to pay closer attention to your attitudes and to intentionally increase your humbleness.
The path of self purification is not such that a person can only work on one issue without regard to other aspects. So the general path of purification decreases arrogance as a person becomes more illuminated by the light of faith.
May you always be successful