Applying to firm client

Hi there. I want to apply for a position with a client of my firm. My current firm/SL recently did a lot of work for this client (not me personally). Is there any chance word would get back to my boss(s) that I am applying to this company? I’m worried the client would ask the local office about me.. or is there something I can do with my resume/cover letter to ensure they respect my privacy in this regard? Thank you

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