Regime backing some trite idea (4)
I believe the answer is:
diet
'regime' is the definition.
(I've seen this before)
'backing some trite idea' is the wordplay.
'backing' says the letters should be written backwards.
'some' indicates a hidden word (some of the parts of the word are used).
'teid' can be found hidden inside 'trite idea'.
'teid' written backwards gives 'DIET'.
(Other definitions for diet that I've seen before include "prescribed nourishment?" , "What one normally eats" , "Special food regime" , "control weight" , "Attempt to shift a few pounds" .)