The poet yearns for a rhyme (5)
I believe the answer is:
burns
'the poet' is the definition.
(Rabbie Burns 1759-1796 the Scottish poet)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for burns that I've seen before include "Cremates -- Scottish poet, d.1796" , "Tam o' Shanter poet, d. 1796" , "experiences strong emotion" , "is full of passion" , "Is on fire" .)