explore has 2 distinct synonyms spread across 1 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.
inquire into
“the students had to research the history of the Second World War for their history project”
travel to or penetrate into
“explore unknown territory in biology”
examine (organs) for diagnostic purposes
Synonyms, antonyms and the broader and narrower relations for explore come from Princeton University’s WordNet. Full sources and licences.