Criminals being executed? They start off being first rankers (5)
I believe the answer is:
rooks
'they start off being first rankers' is the definition.
(rooks are positioned on the first rank in chess)
'criminals being executed?' is the wordplay.
'criminals' becomes 'crooks' ('crook' can be a synonym of 'criminal').
'being executed?' means to remove the first letter (the word is beheaded).
'crooks' with its initial letter removed is 'ROOKS'.
(Other definitions for rooks that I've seen before include "men on the board" , "Overcharges" , "Chess castles and birds" , "Collective name for them is a parliament" , "Large, crow-like birds" .)