engagement has 15 distinct synonyms spread across 7 of its 7 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is non-engagement.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
a hostile meeting of opposing military forces in the course of a war
“Grant won a decisive victory in the battle of Chickamauga”
a meeting arranged in advance
“she asked how to avoid kissing at the end of a date”
the act of giving someone a job
employment for performers or performing groups that lasts for a limited period of time
“the play had bookings throughout the summer”
contact by fitting together
“the engagement of the clutch”
the act of sharing in the activities of a group
“the teacher tried to increase his students' engagement in class activities”
Synonyms, antonyms and the broader and narrower relations for engagement come from Princeton University’s WordNet. Full sources and licences.