hard-nosed (10)
(Other definitions for headstrong that I've seen before include "Wilfully determined" , "strong-willed" , "obstinately self-willed" , "pig-headed" , "Obstinate" .)
'hard-nosed' is the definition.
(I've seen this in another clue)
This is the entire clue.
(Other definitions for stern that I've seen before include "Grave; rear" , "Rear of a vessel" , "Forbidding, austere" , "Strict - forbidding" , "Forbidding in aspect" .)