"Imprest up on" is a fairly uncommon phrase, but it can be broken down into two separate words with more common synonyms. "Imprest" can mean an advance or a loan, while "up on" can mean informed or knowledgeable. Therefore, some synonyms for "imprest up on" could be: briefed, informed, advanced, loaned, supplied, funded, given notice, educated, instructed, or in the loop. Depending on the context of the phrase, other synonyms like "up to date," "current," or "informed of the situation" could also be applicable. It's important to consider the desired meaning and how it fits into the overall sentence when choosing a synonym for "imprest up on".