Rat, possibly, in rubbish outside study (6)
I believe the answer is:
rodent
'rat possibly' is the definition.
(rat is a kind of rodent)
'rubbish outside study' is the wordplay.
'rubbish' becomes 'rot' (both can mean nonsense).
'outside' indicates putting letters inside.
'study' becomes 'den' (term for a study or office).
'rot' enclosing 'den' is 'RODENT'.
'in' is the link.
(Other definitions for rodent that I've seen before include "Eg, capybara" , "Mouse, squirrel or rat" , "Nibbler" , "E.g. hamster" , "Animal such as a mouse" .)