WordNet sense 1 (reserved in advance):

booked, set-aside

WordNet sense 2 ((of facilities such as telephones or lavatories) unavailable for use by anyone else or indicating unavailability; (`engaged' is a British term for a busy telephone line)):

in use

WordNet sense 3 (held or filled or in use):

occupied

WordNet sense 4 (connected by participation or association or use):

involved

WordNet sense 5 ((used of toothed parts or gears) interlocked and interacting):

intermeshed, meshed

WordNet sense 6 (equipped with or connected by gears or having gears engaged):

geared

WordNet sense 7 (having your services engaged for; or having a job especially one that pays wages or a salary):

employed

WordNet sense 8 (joined or linked together):

connected

WordNet sense 9 (actively or fully engaged or occupied):

busy

WordNet sense 10 (pledged to be married):

affianced, bespoken, betrothed, pledged

WordNet sense 11 (associated in an exclusive sexual relationship):

committed, attached