Wild child is kid getting a cake (10)
I believe the answer is:
ragamuffin
'wild child' is the definition.
'is kid getting a cake' is the wordplay.
'is kid' becomes 'rag' (I've seen this in other clues).
'getting' means one lot of letters go next to another.
'cake' becomes 'muffin' (I've seen this before**).
'rag'+'a'+'muffin'='RAGAMUFFIN'
(Other definitions for ragamuffin that I've seen before include "Unkempt, disreputable child" , "One got up badly" , "Street child" , "untidy child" , "Poor mite" .)