Modest prize money denied entrant in fourth place (4)

I believe the answer is:
pure
'modest' is the definition.
(thesaurus)
'prize money denied entrant in fourth place' is the wordplay.
I cannot really understand how this works, but
'money' could be 'p' and 'p' is found in the answer.
The remaining letters 'ure' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for pure that I've seen before include "Unsoiled" , "Untainted" , "Virginal" , "Innocent, uncontaminated" , "Innocent; unsullied" .)
