Rodent bites small European monkey (8)
I believe the answer is:
marmoset
'monkey' is the definition.
(marmoset is a kind of monkey)
'rodent bites small european' is the wordplay.
'rodent' becomes 'marmot' (marmot is a kind of rodent**).
'bites' indicates putting letters inside.
'small' becomes 's' (abbreviation - e.g. clothes size).
'european' becomes 'e' (abbreviation e.g. EU).
's'+'e'='se'
'marmot' going around 'se' is 'MARMOSET'.
(Other definitions for marmoset that I've seen before include "Star memo about kind of monkey" , "Monkey with claws" , "Take me to arms about bushy-tailed monkey of tropical America" , "Somme rat? (anag)" , "Turn morse mat over for the monkey" .)