Synonyms for Quarter:

adj.

fractional (adjective)
sectional, segmental, fragmentary, half, fractional, third, part, semi.
regional (adjective)
provincial, riding, area, borough, colonial, commonwealth, city, precinct, circuit, shire, territorial, divisional, sector, canton, local, district, state, zone, national, realm, tract, regional, town, county.

n.

biannual, calendar, academic year, BCE, semester, C, span, 00s, B, annual, BC. after, forward, coin, money, half-hour, at, two bits, around, ahead, fast, about, AM. belt, neck of the woods, BMI, Centigram, carat, cubic, acre, are, bushel, cu. berth, assemblage, age group, crush, collection, protection, accommodate, array, busload, bunk, domicile, put up, constellation, harbor, crowd, circle, board, room, bestow, club. barrio, block, armpit, brownfield, agora, cabbagetown, burbs, cantonment. generosity, solicitude, kindness, support, altruism, hospitality, liberality, consideration, warmth. common fraction, fifth, eleventh, fiftieth, billionth, eighth, fifteenth, common denominator, And. crown, dollar, dime, euro, bit, ct, dinar, cent, Aud. detail, dog tag, bust, fort, base, generalship, garrison, fatigues. first half, halftime, extra time, run-in, break, injury time, pregame, overtime. cut, etch, clip, hack, chop, cut out, cut-up, finely. area (noun)
city, county, belt, plot, field, parcel, kingdom, tract, neighborhood, block, state.
at close range (noun)
restricted, near, cramped, close together.
direction (noun)
direction, point, bearing.
fraction (noun)
half, third, part, section, denominator, portion, fraction, numerator, segment, piece, slice, fragment, chunk.
geographical area (noun)
district.
mercy (noun)
mercy, indulgence, compassion, clemency.
quarter (noun)
direction, sector, section, portion, point, region, domain, span, locale, compassion, two bits, place, semester, bearing, district, division, neck of the woods, precinct, province, zone, locality, mercy, barrio, part, territory, area, clemency.
quarters (noun)
room, roost, cantonment.
region (noun)
commonweal, territory, division, place, riding, dukedom, canton, colony, precinct, realm, tract, kingdom, lot, empire, neighborhood, beat, province, locality, country, domain, field, sector, county, city, earldom, bailiwick, shire, municipality, state, parcel, nation, town, circuit, duchy, borough, plot.

v.

cut (verb)
hack, slice, clip.
occupy (verb)
dwell, house, billet, roost, inhabit, reside, lodge, stay, occupy, colonize, squat.
quarter (verb)
billet, harbor, cut, lodge, house, canton, quadrisect, bunk, board, domicile, accommodate, put up.

Other synonyms:

first half, pregame, mercy, extra time, halftime, injury time. domicile, overtime, neck of the woods, cut, run-in. bunk, board, belt, accommodate. harbor. bestow. break. live in
dwell.
Other relevant words:
board, chop, berth, halftime, harbor, accommodate, block, liberality, clemency, cantonment, indulgence, bunk, compassion, point, semester, consideration, run-in, crown, detail, two bits, generosity, pregame, dime, circle, cut, bearing, overtime, belt, direction, neck of the woods, kindness, barrio, dollar, domicile, span, bestow, academic year, cent, mercy, room.