apply has 12 distinct synonyms spread across 7 of its 10 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.
be applicable to; as to an analysis
“This theory lends itself well to our new data”
give or convey physically
“She gave him First Aid”
refer (a word or name) to a person or thing
“He applied this racial slur to me!”
apply oneself to
“Please apply yourself to your homework”
Synonyms, antonyms and the broader and narrower relations for apply come from Princeton University’s WordNet. Full sources and licences.