Synonyms for Engagement (same or very similar meaning)
WordNet sense 1 (a meeting arranged in advance):
appointment, date
WordNet sense 2 (contact by fitting together):
interlocking, mesh, meshing
WordNet sense 3 (a mutual promise to marry):
betrothal, troth
WordNet sense 4 (the act of sharing in the activities of a group):
involution, involvement, participation
WordNet sense 5 (the act of giving someone a job):
employment
WordNet sense 6 (a hostile meeting of opposing military forces in the course of a war):
battle, conflict, fight, conflict
WordNet sense 7 (employment for performers or performing groups that lasts for a limited period of time):
booking
From the ODE community, based on WordNet
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