Those backing hopeless idea off Blue Peter (4)
I believe the answer is:
safe
'peter' is the definition.
(slang term)
'those backing hopeless idea off blue' is the wordplay.
'those backing' says to take the final letters (letters at the back).
The final letters of 'hopeless idea off blue' are 'SAFE'.
(Other definitions for safe that I've seen before include "Reliable" , "Metal container for valuables" , "Uninjured; excellent; lockable cabinet" , "Iron box in which to keep money or important papers" , "Out of harm's way" .)