Furious cook with extremely antisocial air (8)
I believe the answer is:
madrigal
'air' is the definition.
(I've seen this before)
'furious cook with extremely antisocial' is the wordplay.
'furious' becomes 'mad' (I've seen this in another clue).
'cook' becomes 'rig' (I've seen this in other clues).
'with' means one lot of letters go next to another.
'extremely' suggests removing the centre (only the extremes of the word are used).
'antisocial' with its middle removed is 'al'.
'mad'+'rig'+'al'='MADRIGAL'
(Other definitions for madrigal that I've seen before include "Elaborate part song" , "Part-song" , "Drag Liam around to hear an unaccompanied song" , "Part song for unaccompanied voices" , "glee" .)