Sexual abstinence, abstention or restraint: the practice of refraining/abstaining from sexual relations/some or all aspects of sexual activity for any reason.
Dictionarized adjectivals (abstainer, abstinent, abstentious, abstemious) in English are commonly associated with abstention from ingestion/consumption (not consummation), while some alternatives can be used for general abstention: abstentioned, abstentioner, restrained, restrainer, abstemic, abstent/abstant (abstence/abstance), abstential/abstemial.
Abstention can be temporary, lasting, voluntary, involuntary, quoiluntary, etc. Usually it’s associated with religion/spirituality, but there are other reasons someone could personally abstain from sex: medical, psychological, legal, social, financial, philosophical, moral...
Both chastities and celibacies can be/are forms of sexual abstention/abstinence, while not all abstentions are considered celibate/chaste. Not the same as asexuality, as abstinence is behavioral.