Hi Jennifer,
It sounds great that you have found a supervisor who is happy for her to add her name to your application as a supervisor for postgraduate study. I'm not sure if it guarantees your entry to the university as you would still need to go through the application and possibly interview process as well. From my own experience, I needed to find a potential supervisor who was happy to work with me in order to apply. Once I applied I then had an interview with other tutors in the faculty. In the interview I talked about the research plan I had submitted and explained what I wanted to research and why this built upon existing work in the field already, and also how I would be contributing to this research already out there. Finding a supervisor is the first step, but it's great you have found a supervisor who obviously likes your ideas,
Good luck with your application,
Best wishes
Jess
PhD English
University of Chester