Singular male irritates: giving smug looks (6)
I believe the answer is:
smirks
'smug looks' is the definition.
(I've seen this in another clue)
'singular male irritates' is the wordplay.
'singular' becomes 's' (abbreviation sometimes used in dictionaries).
'male' becomes 'm' (common abbreviation).
'irritates' becomes 'irks' (I've seen this in another clue).
's'+'m'+'irks'='SMIRKS'
'giving' is the link.
(Other definitions for smirks that I've seen before include "Conceited smiles" , "Smiles foolishly" , "Smiles smugly" , "grins" .)