Mouse for example, with lair surrounded by rubbish (6)
I believe the answer is:
rodent
'mouse for example' is the definition.
(I know that mouse is a type of rodent)
'lair surrounded by rubbish' is the wordplay.
'lair' becomes 'den' (synonyms).
'surrounded by' is an insertion indicator.
'rubbish' becomes 'rot' (both can mean nonsense).
'den' inserted within 'rot' is 'RODENT'.
'with' is the link.
(Other definitions for rodent that I've seen before include "Mouse, squirrel or rat" , "Eg, mouse or rat" , "Toothy mammal" , "Mouse or squirrel, say" , "Rat perhaps" .)