Wally always got stuck into state, solemnly (10)
I believe the answer is:
asseverate
'state solemnly' is the definition.
(to asseverate is to declare something solemnly)
'wally always got stuck into' is the wordplay.
'wally' becomes 'ass' (both can mean a stupid person).
'always' becomes 'ever' (synonyms).
'got stuck into' becomes 'ate' (to get stuck into can mean to eat).
'ass'+'ever'+'ate'='ASSEVERATE'
(Other definitions for asseverate that I've seen before include "Swear" , "State categorically" , "Claim" , "Solemnly say" , "Solemnly declare" .)