govern has 5 distinct synonyms spread across 2 of its 4 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. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
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.
bring into conformity with rules or principles or usage; impose regulations
“We cannot regulate the way people dress”
Synonyms, antonyms and the broader and narrower relations for govern come from Princeton University’s WordNet. Full sources and licences.
direct or strongly influence the behavior of
“His belief in God governs his conduct”
require to be in a certain grammatical case, voice, or mood
“most transitive verbs govern the accusative case in German”