exempt has 5 distinct synonyms spread across 3 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. Its 2 recorded opposites are enforce, nonexempt.
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.
grant relief or an exemption from a rule or requirement to
“She exempted me from the exam”
(of persons) freed from or not subject to an obligation or liability (as e.g. taxes) to which others or other things are subject
“a beauty somehow exempt from the aging process”
(of goods or funds) not subject to taxation
“the funds of nonprofit organizations are nontaxable”
Synonyms, antonyms and the broader and narrower relations for exempt come from Princeton University’s WordNet. Full sources and licences.