A lot of the slate we run into has a top coat. Customer wanted it to shine. figure out if this one does by scraping it with a razor in a corner some where inconspicuous. If it does and after a cleaning test it still looks dirty you can run or attempt to be the hero and strip it. Seeing how you are asking this question. I would suggest you run.
Other wise clean with any alkaline PS with a oxygen boost use any solvent based sealer.
Enhancing is popular with slate but not some thing a first timer should try