A very incomplete state (4)
I believe the answer is:
aver
'state' is the definition.
(both can mean to declare)
'a very incomplete' is the wordplay.
'incomplete' means to remove the last letter.
'very' with its final letter removed is 'ver'.
'a'+'ver'='AVER'
(Other definitions for aver that I've seen before include "Declare < old cattle" , "Assert to be the case" , "Declare positively" , "Profess" , "State firmly, propound" .)