Encourage man perhaps painting Euston externally (7)
I believe the answer is:
hearten
'encourage' is the definition.
(I know that hearten is a more specific form of the action encourage)
'man perhaps painting euston externally' is the wordplay.
'man' becomes 'he' (he refers to a man).
'perhaps painting' becomes 'art' (painting is a kind of art).
'externally' says to hollow out the word (remove centre letters) (only the external letters are used).
'euston' with its centre removed is 'en'.
'he'+'art'+'en'='HEARTEN'
(Other definitions for hearten that I've seen before include "given cheer" , "Comfort" , "Make cheerful" , "Inspirit" , "Encourage in Teheran" .)