What to do with browned butter after frying a steak
Often, assuming they are not too burned, you would make a simple pan sauce from the fond and fat left after pan-cooking a steak.  Methods vary, but might include sauteeing some shallots or onions in the fat, deglazing with wine, and/or adding a slurry of flour to thicken.  You would then serve with the steak.

Other than this, there is no general purpose use for the left over pan drippings.