With no exceptions, rigorously (8)
I believe the answer is:
strictly
This clue is a double definition.
'with no exceptions' is the first definition.
(I've seen this before)
'rigorously' is the second definition.
(I know that rigorously can be written as strictly)
(Other definitions for strictly that I've seen before include "-- Come Dancing" , "Precisely and severely" , "Allowing no exception as in business" , "Stringently, rigidly" , "In a rigorous manner" .)