This account is not always strictly truthful (7)
I believe the answer is:
expense
'this account' is the definition.
(expense account is a kind of account)
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for expense that I've seen before include "Cost - price" , "damage" , "Money spent in the course of work" , "Disbursal" , "Disbursement" .)