Specific demand (5)
I believe the answer is:
exact
I believe this clue is a double definition.
'specific' is the first definition.
(I've seen this before)
'demand' is the second definition.
(exacting is a kind of demanding)
(Other definitions for exact that I've seen before include "Precise - demand" , "Precise and strictly correct" , "Explicit" , "As a right, demand" , "Absolutely right" .)