Rigorous check requires coupon in order to set up deposit account (4,4)
I believe the answer is:
acid test
'rigorous check' is the definition.
(an acid test is a conclusive test of something)
'coupon in order to set up deposit account' is the wordplay.
I cannot quite see how this works, but
an anagram of 'set' is 'tes' which is within the answer.
'account' could be 'ac' (abbreviation for account) and 'ac' is found in the answer.
This may be the basis of the clue (or it may be nonsense).
'requires' acts as a link.
(Other definitions for acid test that I've seen before include "Validity confirmed" , "Conclusive moment (using litmus paper?)" , "Conclusive trial of success or value" , "Dictates to undergo conclusive trial" , "A severe or conclusive exam or trial" .)