Most orderly trial with papers I lodged (7)
I believe the answer is:
tidiest
'most orderly' is the definition.
('tidy' is associated in meaning with 'orderly')
'with papers i lodged' is the wordplay.
'with' means one lot of letters goes inside another.
'papers' becomes 'ID' (identification papers).
'lodged' becomes 'test' (I can't explain this - if you can you should give a lot more credence to this answer).
'id'+'i'='idi'
'idi' placed inside 'test' is 'TIDIEST'.
'trial' acts as a link.
I am not very happy about this link. It may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for tidiest that I've seen before include "Neatest" , "Extremely organised" , "smarter than anything" , "optimally arranged" , "most trim" .)