One eager to go outside is putting coat on (8)
I believe the answer is:
painting
'outside is putting coat on' is the definition.
I can't tell whether this definition defines the answer.
'one eager to go' is the wordplay.
'one eager' becomes 'pain' (I can't justify this - if you can you should give a lot more credence to this answer).
'to go' becomes 'ting' (tinging is a kind of going).
'pain'+'ting'='PAINTING'
Can you help me to learn more?
(Other definitions for painting that I've seen before include "Constable possibly" , "Artistic work" , "Work of a kind" , "picture" , "Work of art" .)