Wizard has primate nearly in a fury (9)

'wizard' is the definition.
(term for a great wizard)

'primate nearly in a fury' is the wordplay.
'primate' becomes 'chimp' (short for chimpanzee).
'nearly' means to remove the last letter.
'in' means one lot of letters goes inside another.
'fury' becomes 'rage' (synonyms).
'chimp' with its last letter removed is 'chim'.
'a'+'rage'='arage'
'chim' put inside 'arage' is 'ARCHIMAGE'.

'has' acts as a link.