Poet's endless stream (4)
I believe the answer is:
burn
'stream' is the definition.
(a burn is a small stream)
'poet's endless' is the wordplay.
'poet' becomes 'burns' (Rabbie Burns 1759-1796 the Scottish poet).
'endless' means to remove the last letter.
'burns' with its final letter taken off is 'BURN'.
(Other definitions for burn that I've seen before include "Heat injury; stream" , "Go up in smoke" , "Catch fire; small stream" , "Incinerate" , "runner?" .)