Poet possibly born around the end of the century (5)
I believe the answer is:
byron
'poet' is the definition.
(Lord Byron)
'possibly born around the end of the century' is the wordplay.
'possibly' indicates anagramming the letters.
'around' indicates putting letters inside.
'the end of the' indicates one should take the final letters.
The last letter of 'century' is 'y'.
'born' is an anagram of 'bron'.
'bron' enclosing 'y' is 'BYRON'.
(Other definitions for byron that I've seen before include "Author of 'Don Juan'" , "Eng. romantic poet (Don Juan)" , "Lord . . . . ., English poet who wrote 'Childe Harold's Pilgrimage'" , "English poet, said to be 'mad, bad, and dangerous to know', d. 1824" , "Lord George, poet" .)