Man shot some rat and monkey (8)
I believe the answer is:
marmoset
'monkey' is the definition.
(marmoset is a kind of monkey)
'man shot some rat' is the wordplay.
'man' becomes 'm' ().
'shot' is an anagram indicator.
'some'+'rat'='somerat'
'somerat' with letters rearranged gives 'armoset'.
'm'+'armoset'='MARMOSET'
'and' acts as a link.
(Other definitions for marmoset that I've seen before include "Somme rat? (anag)" , "rather small creature" , "Take me to arms about bushy-tailed monkey of tropical America" , "Small monkey - Rome's mat (anag)" , "Star memo about kind of monkey" .)