Man with fair promotion prospects given hand by Pole (6,4)
I believe the answer is:
passed pawn
'man with fair promotion prospects' is the definition.
(in chess, a pawn likely to be promoted)
'given hand by pole' is the wordplay.
'given' becomes 'passed' ('pass' can be a synonym of 'give').
'hand by' becomes 'paw' (synonyms. I am not sure about the 'by' bit.).
'pole' becomes 'n' (abbreviation for North, as in North Pole).
'passed'+'paw'+'n'='PASSED PAWN'
Can you help me to learn more?
(Another definition for passed pawn that I've seen is " Potential queen".)