Sportsman having a fling (7)
I believe the answer is:
pitcher
'sportsman' is the definition.
(I have seen 'American sportsman' mean 'pitcher' so perhaps 'sportsman' could also mean 'pitcher')
'a fling' is the wordplay.
I cannot quite understand how this works, but
'fling' could be 'pitch' (pitching is a kind of flinging) and 'pitch' is found in the answer.
The remaining letters 'er' 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).
'having' acts as a link.
Can you help me to learn more?
(Other definitions for pitcher that I've seen before include "One throwing" , "Someone promoting" , "Baseball bowler and vessel for liquid" , "US sportsman" , "Vessel with a handle and spout" .)