Antipodean recognised headless spirit with sign of hesitancy (3,9)
I believe the answer is:
new zealander
'antipodean' is the definition.
(I know that New Zealander is a type of antipodean)
'recognised headless spirit with sign of hesitancy' is the wordplay.
'recognised' becomes 'knew' (know can mean to recognise someone).
'headless' means to remove the first letter.
'spirit' becomes 'zeal' (I've seen this in another clue).
'with' becomes 'and'.
'sign of hesitancy' becomes 'er' (sound made when hesitating).
'knew' with its initial letter removed is 'new'.
'new'+'zeal'+'and'+'er'='NEW ZEALANDER'
(Other definitions for new zealander that I've seen before include "Kiwi" , "Native of the Antipodes" , "Man from island" , "Inhabitant of Wellington?" , "Enzedder" .)