persevere in (something)
To continue trying to improve at or succeed in doing something. Your writing isn't going to be amazing when you first start—you have to persevere in it. Even though I struggled at times, I persevered in my studies and ended up graduating with a 3.5 GPA.
persevere in something
to persist in [doing] something. I will persevere in my efforts to win election. Kelly persevered in her studies and graduated with honors.