Look to make a new hat out of leather (4)
I believe the answer is:
leer
'look' is the definition.
(leer is a kind of look)
'hat out of leather' is the wordplay.
'out of' indicates named letters should be taken away ('out of' can mean no longer having).
'leather' with 'hat' taken out is 'LEER'.
'to make a new' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for leer that I've seen before include "Stare suggestively" , "Ogle, smirk" , "Suggestive or sneering grin" , "Gaze lasciviously at" , "Look lecherously" .)