It sounds like a specific role within a team, but it is not one I have heard of and only "Distribution Process Advocate" gets much in the way of Google hits (and there are only 68 of them), suggesting it is not a common term. It was probably thought up by whoever created the procedure, and I would expect the term to be defined elsewhere in the document you quote from.
A process advocate seems to be a specialist in the rules and regulations of a particular (especially specialised) process or area of commerce. The process advocate will ensure that the rules and regulations surrounding the process are adhered to by both parties to a contract.
Although the term implies (via advocate) that the person will be some type of lawyer, this is not always a requirement where experience is sufficient.