Notice Tim returning and let him in (5)
I believe the answer is:
admit
'let him in' is the definition.
'admit' can be an answer for 'let' (admitting is a kind of letting). I am unsure of the 'him in' bit.
'notice tim returning' is the wordplay.
'notice' becomes 'ad' (short for advert).
'returning' shows that the letters should be reversed in order.
'tim' back-to-front is 'mit'.
'ad'+'mit'='ADMIT'
'and' acts as a link.
Can you help me to learn more?
(Other definitions for admit that I've seen before include "permit to come in" , "Stop being obstructive" , "Profess" , "Come clean" , "Agree to the truth" .)