Look after the intellect (4)
I believe the answer is:
mind
This clue is a double definition.
'look after' is the first definition.
(I've seen this in another clue)
'the intellect' is the second definition.
(mind is a kind of intellect)
(Other definitions for mind that I've seen before include "'Out of sight, out of ....'" , "remember" , "Intelligence" , "Look after" , "Object to; take care of" .)