Engaged
occupied, diligent, working, employed, involved, tied up, in conference, in a meeting, in the field, on an assignment; with a customer, with a patient, etc.; on duty, on the job, at work, on the move, on the run, on the road, hard-working, industrious, buried in, busy as a bee*, hustling*, up to one's ears, up to one's neck, up to one's eyeballs*, on the go*, on the jump*, hard at it*, having many irons in the fire*, having other fish to fry*; see also employed.
Antonyms idle, unemployed*, unoccupied, free.