Tutor taking hour off with first kid in A&E gets something nice to eat (3,4)
I believe the answer is:
tea cake
'kid in ae gets something nice to eat' is the definition.
I can't tell whether this definition defines the answer.
'tutor taking hour off with' is the wordplay.
'tutor' becomes 'teach' (I've seen this in another clue).
'taking' suggests deleting specific letters (take can mean remove or delete).
'hour' becomes 'h' (abbreviation).
'off with' becomes 'ake' (I am not sure about this - if you are sure you should believe this answer much more).
'teach' with 'h' taken away is 'teac'.
'teac'+'ake'='TEA-CAKE'
'first' is the link.
Can you help me to learn more?
(Other definitions for tea cake that I've seen before include "bun" , "Buttery snack" .)