Insist upon being strict (5)
I believe the answer is:
exact
This clue is a double definition.
'insist upon' is the first definition.
(thesaurus)
'strict' is the second definition.
('exact' can be similar in meaning to 'strict')
'being' is the link.
(Other definitions for exact that I've seen before include "Explicit" , "Precisely accurate" , "totally accurate" , "Absolutely right" , "Demand and obtain" .)