Yes, or you could also say any of the following:
1. To obtain a position in which I can use my prior experience to contribute to an university and grow both individually and professionally.
2. To obtain a position in which I can use my prior experience to contribute to an university and grow both on a personal and a professional level.
* I would say "contribute to" or "contribute within" as Rachael said.
* If you mean a specific university, then I guess I would go with "the University"; otherwise, I would go with "an university". I think in most American resumes we write a goal at the top which doesn't mention the place in particular that you are applying to. So "to obtain a position at a company where...". If this were a cover letter where you are speaking about the actual place though, then I would use "the." Hmmm.