enter has 19 distinct synonyms spread across 8 of its 9 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 2 recorded opposites are exit, drop out.
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.
become a participant; be involved in
“enter a race”
take on duties or office
“accede to the throne”
1 of the 9 recorded senses carries no synonym, antonym or related term, so it is not shown above. Every sense, with its definition and examples, is on the full entry for enter.
Synonyms, antonyms and the broader and narrower relations for enter come from Princeton University’s WordNet. Full sources and licences.