Accept endless cant swallowing falsehood (7)
I believe the answer is:
believe
'accept' is the definition.
(believing is a kind of accepting)
'endless cant swallowing falsehood' is the wordplay.
'endless' means to remove the last letter.
'cant' becomes 'bevel' ('bevel' can be a synonym of 'cant').
'swallowing' is an insertion indicator.
'falsehood' becomes 'lie' (lie is a kind of falsehood).
'bevel' with its last letter removed is 'beve'.
'beve' enclosing 'lie' is 'BELIEVE'.
(Other definitions for believe that I've seen before include "Swallow" , "Have confidence in" , "Regard as true" , "Accept as true" , "Have faith; accept" .)