Criminal has no right to be captain (4)
I believe the answer is:
cook
'be captain' is the definition.
(captain james cook)
'criminal has no right' is the wordplay.
'criminal' becomes 'crook' ('crook' can be a synonym of 'criminal').
'has no' is a deletion indicator.
'right' becomes 'r' (common abbreviation).
'crook' with 'r' removed is 'COOK'.
'to' acts as a link.
(Other definitions for cook that I've seen before include "18th-century explorer" , "Capt. James --, explorer" , "Prepares a hot meal" , "spoil" , "Heat food" .)