Looked at assessment and longed to leave quietly (8)
I believe the answer is:
examined
'looked at' is the definition.
('examine' can be a synonym of 'look at')
'assessment and longed to leave quietly' is the wordplay.
'assessment' becomes 'exam'.
'and' says to put letters next to each other.
'longed' becomes 'pined' ('pine' can be a synonym of 'long').
'to leave' is a deletion indicator.
'quietly' becomes 'p' (p for piano and quiet).
'pined' with 'p' taken out is 'ined'.
'exam'+'ined'='EXAMINED'
(Other definitions for examined that I've seen before include "Questioned or inspected" , "Questioned, tested" , "I need Max to be tested" , "Looked into something closely" , "Tested or scrutinised" .)