Had a fling (5)
I believe the answer is:
threw
'had' is the definition.
('throw' can be a synonym of 'have')
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for threw that I've seen before include "Disconcerted" , "Propelled through the air" , "Bowled unfairly" , "Projected through the air" , "Confused" .)