On green, one may gamely hope not to do so thrice (4)
I believe the answer is:
putt
'on green one' is the definition.
Although both the answer and definition are singular nouns, I can't see how one could define the other.
'gamely hope not to do so thrice' is the wordplay.
I cannot quite understand how this works, but
'do' could be 'ut' (both can mean the first note in a musical scale) and 'ut' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'may' acts as a link.
Can you help me to learn more?
(Other definitions for putt that I've seen before include "Stroke which hopefully sinks" , "Green shot" , "Final stroke of hole" , "Golf stroke near hole" , "Play ball on green" .)