Member a Green brought into party is a beast (9)
I believe the answer is:
armadillo
'beast' is the definition.
(armadillo is a kind of beast)
'member a green brought into party' is the wordplay.
'member' becomes 'arm' (member can mean a limb).
'green' becomes 'ill' (eg looking green means looking ill).
'brought into' indicates putting letters inside.
'party' becomes 'do' (do is a kind of party).
'ill' placed inside 'do' is 'dillo'.
'arm'+'a'+'dillo'='ARMADILLO'
'is a' is the link.
(Other definitions for armadillo that I've seen before include "Long-snouted animal" , "Nocturnal creature" , "Scaly mammal" , "Animal covered with long plates" , "Nocturnal animal" .)