Synonyms for Abstinent:

adj.

abstemious (adjective)
frugal, self-denying, sober, austere, moderate, temperate, ascetic, restrained.
ascetic (adjective)
abstemious, severe, stark, stoic, franciscan, miserly, austere, parsimonious, repentant, celibate, lenten, trappist, penitential, spartan, monastic, dry, teetotaling, hermit-like, ascetic.
celibate (adjective)
maiden, ascetic, asexual, intact, old maid, bachelor, single, unplowed, lone, virginal, monkish, alone, unwed, celibate, solitary, chaste, unmarried, abstemious, monastic, spinsterish, pure.
continent (adjective)
abstentious, celibate.
moderate (adjective)
conservative.
on the wagon (adjective)
dry.
sober (adjective)
teetotaling, temperate, sober, dry, restrained, moderate.
temperate (adjective)
conservative, austere, restrained, prudent, self-denying, Sober-minded, moderate, temperate, sober, self-depriving, Abnegating, ascetic, frugal.

n.

abstainer (noun)
nondrinker.
abstinent (noun)
abstemious, abstainer, nondrinker, abstentious.
person (noun)
abstainer, nondrinker.
teetotaler (noun)
abstainer.

Other synonyms:

nondrinker
nondrinker.
Other relevant words:
abstentious, nondrinker, abstainer.