Ruthless (4-5)
'ruthless' is the definition.
(I've seen this before)
This is the entire clue.
(Other definitions for dog-eat-dog that I've seen before include "Ruthless competition of canine cannibals" , "Internecine competition" , "Savagely ruthless" , "Ruthless competition - savage self-concern" , "Ruthless competition like canine cannibalism" .)
(Other definitions for hard-nosed that I've seen before include "Realistic and tough-minded" , "Tough and uncompromising" , "Unsentimental, shrewd" .)