Synonyms for Engage:

n.

motivate, reserve, fire someone with enthusiasm, dazzle, enthuse, inspire, attract. belligerent, battle cry, black out, Beleaguered, active duty, aggressor, air cover, attack, assault, bombed-out, active service. confirm, join, sign on, appoint. bespeak, book. agree, promise, obligation. excite. draw in, participate. carry on, partake, indulge. action. preempt, used, tie up, monopolize. encounter, meet. connect. engage (noun)
lease, affiance, occupy, absorb, hire, retain, lock, engross, betroth, take, rent, pursue, mesh, charter, wage, enlist, plight, operate, prosecute.

v.

battle (verb)
contest, conflict, drive, fight, struggle, battle, scramble, combat, campaign, scuffle, tussle.
cognition (verb)
absorb, occupy, engross.
endeavor (verb)
undertake, contract, perform, endeavor, venture, maneuver, assay, aim, approach, commit, attempt, exploit, act, volunteer, proceed.
hire (verb)
employ, rent, lease.
hire for job, use (verb)
charter, book, enlist, retain, employ, rent, reserve, contract, bespeak, lease, sign on, appoint.
interconnect; bring into operation (verb)
energize, lock, mesh, activate.
occupy oneself; engross (verb)
join, tie up, monopolize, bewitch, captivate, participate, partake, undertake, fascinate, absorb.
promise to marry (verb)
agree, betroth, commit, affiance.
social (verb)
prosecute, pursue.
start a fight; attack (verb)
combat, encounter, meet, assault.

Other synonyms:

actuate, sign on, activate, flick, coax. energize, participate, crank, bespeak, monopolize, promise. partake, preempt. book, encounter, confirm. flash, reserve. meet. indulge. charm
fascinate.
charter
lease.
indicate
bespeak.
marry
betroth.
retain
retain.
take
take.

Usage examples for engage

  1. I was not prepared at the moment to give precisely that proof, and he followed up his blow by telling me that, if I wished it, he would engage to secure her for me before the next morning. – Incidents of Travel in Greece, Turkey, Russia, and Poland, Vol. I (of 2) by John Lloyd Stephens
  2. I dare not engage in this! – The Sea-Hawk by Raphael Sabatini