carrot 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.
deep orange edible root of the cultivated carrot plant
perennial plant widely cultivated as an annual in many varieties for its long conical orange edible roots; temperate and tropical regions
orange root; important source of carotene
promise of reward as in "carrot and stick"
“used the carrot of subsidized housing for the workers to get their vote”
Synonyms, antonyms and the broader and narrower relations for carrot come from Princeton University’s WordNet. Full sources and licences.