solicit has 7 distinct synonyms spread across 3 of its 5 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.
incite, move, or persuade to some act of lawlessness or insubordination
“He was accused of soliciting his colleagues to destroy the documents”
make a solicitation or petition for something desired
“She is too shy to solicit”
Synonyms, antonyms and the broader and narrower relations for solicit come from Princeton University’s WordNet. Full sources and licences.