Cat perhaps with need to chew piece of material (7)
I believe the answer is:
placket
'material' is the definition.
(placket is a kind of material)
'cat perhaps with need' is the wordplay.
'cat perhaps' becomes 'pet' (cats are kept as pets).
'with' means one lot of letters goes inside another.
'need' becomes 'lack' (to lack something is to be in need of it).
'pet' placed around 'lack' is 'PLACKET'.
'to chew piece of' 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 placket that I've seen before include "Piece of cloth" , "opening" .)