From Longman Business Dictionaryhead up phrasal verb1[transitive] head something → upJOB to be in charge of an organization, part of an organization, or a groupPerkins left his post to head up marketing at Pizza Hut.2[intransitive] (also be headed up)FINANCE if a share price, currency etc heads up or is headed up, it increases in valueCommodity prices began heading up just after the recession ended. → head→ See Verb table