He's simply a nursery-rhyme character (5)
I believe the answer is:
simon
'character' is the definition.
(I know that Simon is a human biblical figure)
'he's simply a nursery-rhyme' is the wordplay.
I cannot really understand how this works, but
'he' could be 'sim' and 'sim' is found in the answer.
The remaining letters 'on' is a valid word which might be clued in a way I don't see.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for simon that I've seen before include "Bolivar, de Montfort, Callow or Cowell?" , "One of Christ's apostles" , "- and Garfunkel" , "A simple character in nursery rhyme" , "Peter (NT)" .)