Thread from sack catching tip of briar (5)
I believe the answer is:
fibre
'thread' is the definition.
(I've seen this in another clue)
'sack catching tip of briar' is the wordplay.
'sack' becomes 'fire' (both can mean to dismiss from a job).
'catching' is an insertion indicator.
'tip of' suggests taking the first letters.
The initial letter of 'briar' is 'b'.
'fire' going around 'b' is 'FIBRE'.
'from' acts as a link.
(Other definitions for fibre that I've seen before include "Thread, strand" , "(Material composed of) thread(s)" , "Coarse plant food, low in nutrients" , "Thread; stamina" , "Long fine thread" .)