I was head-hunted a few years ago for a position at Company A by an executive search/recruitment agency. The agency was very professional and I really liked working with them. The job they found me is great. I've been working in that same position for a few years now (3 years+) and I'm very happy, but I feel like I'm ready to move on to a new more challenging role and to a new company.
I've recently seen an interesting job at Company B advertised on the website of the same recruitment agency that had introduced me to the company that I'm working for right now. I really liked working with them in the past, and would like to work with them again for my current job-hunt.
My question is: can I apply for this new role at company B through the same recruitment agent that had hired me for my current position at company A a few years ago? Or is the recruiter under some sort of obligation to my current employer - Company A*- not to represent me for a new role with another company?