WordNet records no synonym and no antonym for queen regent. It is the only member of its synset, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
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.
a queen who serves as ruler when the king cannot
Synonyms, antonyms and the broader and narrower relations for queen regent come from Princeton University’s WordNet. Full sources and licences.