Applying for a job at a client

so my question is not is it wrong/weird, but rather what risk are you running by applying for an opening at a relatively close client (comes over to our office a few times a yr, they speak regularly with their salesman here who sits 3 cubes away from me). I work in FI S&T at an IB and one our larger customers, an AM firm, that’s in the same city as us (their office really only probably like a few blocks away) has a credit research position open that im interested in, but i dont want to run the risk of them saying something in passing to the guy at my current position that covers them. ive thrown resumes at equity opeinings there before just not FI where there’d be someone who sees it and would have a connection to my current position

Applying with your company’s client is fine. Applying with a firm where your company is their client is not. And I doubt that company will want to burn bridges with your company especially if your company is one of their biggest clients.