external maxillary artery ex·ter·nal·maxillaryartery uncommon noun 1. an artery that originates in the external carotid and gives off branches that supply the neck and face Synonymsfacial arteryarteria facialisexternal maxillary artery Related words Broader terms maxillary artery WordNet 2.1 (Princeton University). WordNet 2.1 Copyright Princeton University. All rights reserved.