quarter has 14 distinct synonyms spread across 4 of its 18 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.
(football, professional basketball) one of four divisions into which some games are divided
“both teams scored in the first quarter”
a unit of time equal to 15 minutes or a quarter of an hour
“it's a quarter til 4”
one of four periods into which the school year is divided
“the fall quarter ends at Christmas”
a fourth part of a year; three months
“unemployment fell during the last quarter”
one of the four major division of the compass
“the wind is coming from that quarter”
a quarter of a hundredweight (25 pounds)
a quarter of a hundredweight (28 pounds)
a United States or Canadian coin worth one fourth of a dollar
“he fed four quarters into the slot machine”
an unspecified person
“he dropped a word in the right quarter”
piece of leather that comprises the part of a shoe or boot covering the heel and joining the vamp
clemency or mercy shown to a defeated opponent
“he surrendered but asked for quarter”
pull (a person) apart with four horses tied to his extremities, so as to execute him
“in the old days, people were drawn and quartered for certain crimes”
Synonyms, antonyms and the broader and narrower relations for quarter come from Princeton University’s WordNet. Full sources and licences.
divide into quarters
“quarter an apple”