Child's play for dad to be gutted in support of the state (6)
I believe the answer is:
doddle
'child's play' is the definition.
(both can mean something very easy)
'dad to be gutted in support of the state' is the wordplay.
'to be gutted' means to remove the middle letters (to gut something is to remove its insides).
'in' is an insertion indicator.
'support of the state' becomes 'dole' (I can't justify this - if you can you should believe this answer much more).
'dad' with its centre removed is 'dd'.
'dd' put within 'dole' is 'DODDLE'.
'for' acts as a link.
Can you help me to learn more?
(Other definitions for doddle that I've seen before include "pushover" , "In slang, an easy task" , "Absurdly simple" , "Easy crossword?" , "Easy task (informal)" .)