Messes about with the covering - paper (8)
I believe the answer is:
foolscap
'paper' is the definition.
(foolscap is a kind of paper)
'messes about with the covering' is the wordplay.
'messes about with' becomes 'fools' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'the covering' becomes 'cap' (cap is a kind of covering).
'fools'+'cap'='FOOLSCAP'
Can you help me to learn more?
(Other definitions for foolscap that I've seen before include "Cop's foal (anag)" , "Paper or book size (from its watermark)" , "type of paper" , "sheet" , "something near A4" .)