Disputing luck could provide a slight possibility of success? (8,6)
I believe the answer is:
fighting chance
'provide a slight possibility of success?' is the definition.
I can't judge whether this definition defines the answer.
'disputing luck' is the wordplay.
'disputing' becomes 'fighting' (I can't explain this - if you can you should give a lot more credence to this answer).
'luck' becomes 'chance' ('chance' can be a synonym of 'luck').
'fighting'+'chance'='FIGHTING CHANCE'
'could' is the link.
Can you help me to learn more?
(Other definitions for fighting chance that I've seen before include "provided by Tweedledum's rattle?" , "Decent prospect" , "Potential for success" , "A possibility of success if great effort is made" , "reasonable prospect" .)