Authority I had for certain material (5)
I believe the answer is:
plaid
'certain material' is the definition.
'plaid' can be an answer for 'material' (plaid is a kind of material). I'm not sure about the 'certain' bit.
'authority i had' is the wordplay.
'authority' becomes 'pla' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'i had' becomes 'I'd' (contraction).
'pla'+'id'='PLAID'
'for' acts as a link.
Can you help me to learn more?
(Other definitions for plaid that I've seen before include "material" , "Cloth for a Highlander" , "Scots cloth - Welsh party" , "Part of Scots dress or Welsh party" , "Tartan patterned cloth" .)