Notice invading stag perhaps cropped corn and look for a man (8,7)
I believe the answer is:
designer stubble
'look for a man' is the definition.
(type of facial hair)
'notice invading stag perhaps cropped corn' is the wordplay.
'notice' becomes 'sign' (I've seen this before).
'invading' means one lot of letters goes inside another.
'stag perhaps' becomes 'deer' (a stag is a male deer).
'cropped corn' becomes 'stubble' (stubble can mean the stalks of cereal plants).
'sign' placed inside 'deer' is 'designer'.
'designer'+'stubble'='DESIGNER STUBBLE'
'and' acts as a link.
(Other definitions for designer stubble that I've seen before include "Fashionable unshaven look" , "shave this?" , "kind of personal appearance" .)