Mean time overseen by state (7)
I believe the answer is:
average
'mean' is the definition.
(synonyms)
'time overseen by state' is the wordplay.
'time' becomes 'age' (an age is a period of time).
'overseen by' means one lot of letters go next to another (in a down clue, some letters go above others).
'state' becomes 'aver' (both can mean to declare).
'age' after 'aver' is 'AVERAGE'.
(Other definitions for average that I've seen before include "Mean - medium" , "Mean - ordinary" , "Arithmetically ordinary?" , "Mediocre - medium" , "Arithmetical mean" .)