Look for private detective (3)
I believe the answer is:
eye
This could be a double definition.
'look' is the first definition.
(I know that eye is a more specific form of look)
'private detective' is the second definition.
'eye' can be an answer for 'detective' (as in a private eye). I'm unsure of the 'private' bit.
'for' is the link.
Can you help me to learn more?
(Other definitions for eye that I've seen before include "9 across village" , "'Please your... and plague your heart'" , "Look at with interest" , "Light-detector" , "One looks" .)