The reason to shift it back inside (6)
I believe the answer is:
motive
'the reason' is the definition.
(I've seen this in another clue)
'shift it back inside' is the wordplay.
'shift' becomes 'move' (I've seen this before).
'back' shows that the letters should be reversed in order.
'inside' means one lot of letters goes inside another.
'it' reversed gives 'ti'.
'move' enclosing 'ti' is 'MOTIVE'.
'to' is the link.
(Other definitions for motive that I've seen before include "Reason for doing something, perhaps a crime" , "Reason behind an action" , "Reason for doing something, say murder" , "Underlying purpose" , "What induces one to take a certain action" .)