This hapax uses the substantival -esse suffix to produce an abstract nominal derivation of prime1. In AND1 the lexeme was glossed as ‘condition of being first-born’, and included in the entry primisces (from Latin primitiae). This association is, however, erroneous on etymological and formal grounds, and therefore the proposed sense is dubious. The Middle English equivalent of this section is hardly a literal translation (power and hardynesse translate primesce and saver), but it supports the idea that primesce may have been a vernacular construction (prime + esse) to express the same meaning as primacie (which retains its more Latinate origin: primatia).
[gdw]