Hi Nsosaz
I don't think I would combine either "previous" or "prior" directly with the word "institution" in a resume.
I might expect to see things such as these, for example:
- My previous employer was ...
- Prior to working at X, I worked at Y.
- At Institution X, I was able to apply and build on the experience I acquired at Institution Y.
I think if you post the whole sentence you want to write, we can give you better feedback.