compensate has 16 distinct synonyms spread across 6 of its 6 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.
make amends for; pay compensation for
“One can never fully repair the suffering and losses of the Jews in the Third Reich”
make up for shortcomings or a feeling of inferiority by exaggerating good qualities
“he is compensating for being a bad father”
Synonyms, antonyms and the broader and narrower relations for compensate come from Princeton University’s WordNet. Full sources and licences.