remit has 14 distinct synonyms spread across 4 of its 9 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.
the topic that a person, committee, or piece of research is expected to deal with or has authority to deal with
“they set up a group with a remit to suggest ways for strengthening family life”
Synonyms, antonyms and the broader and narrower relations for remit come from Princeton University’s WordNet. Full sources and licences.