Let in tiny boy coming back after short notice (5)
I believe the answer is:
admit
'let in' is the definition.
(synonyms)
'tiny boy coming back after short notice' is the wordplay.
'tiny boy' becomes 'Tim' (A Christmas Carol character Tiny Tim).
'coming back' says the letters should be written in reverse.
'after' means one lot of letters go next to another.
'short notice' becomes 'ad' (short for advert; 'short' asks for a short form).
'tim' in reverse letter order is 'mit'.
'mit' after 'ad' is 'ADMIT'.
(Other definitions for admit that I've seen before include "Usher in" , "Confess (to something)" , "permit to come in" , "Confess; allow in" , "Come clean" .)