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An 'anthem' is a sung piece of church music, often a musical setting of a biblical passage. They differ from a hymn in that they are usually musically complex and sung by a choir rather than by the congregation.
Not all services will include a choir, so the anthem is optional. However if one is used, it is sung in the place indicated.
'Quire' is simply an old spelling of 'choir', and the word can be used to mean a place where a choir sings.
So the sentence means:
If you have a choir or other singers, the anthem will be sung at this point in the service.