The adjectives prior and previous are both useful synonyms of earlier and past, and there is no substantive difference between them. Some people do make various distinctions between them in their personal usage, but none of these distinctions are borne out in broader usage. The words are usually interchangeable.
Mayor Robert Dean Smith was arrested Wednesday on allegations he violated a probation from a previous drunken driving conviction. [KJRH.com]
The two have a prior relationship from their days with the New York Giants and will likely play a significant role in offensive game-planning. [Milwaukee Journal Sentinel]
Pawlenty, the previous governor of Minnesota, delivered a speech. [NPR]
In her prior position as San Francisco District Attorney, she was instrumental in securing legal protections for the lesbian, gay, bisexual, and transgender (LGBT) community. [Lez Get Real]