See about painting hospital being feasible (7)
I believe the answer is:
earthly
'being feasible' is the definition.
(thesaurus)
'see about painting hospital' is the wordplay.
'see' becomes 'ely' (example where cathedral located in diocese).
'about' indicates putting letters inside.
'painting' becomes 'art' (I've seen this before).
'hospital' becomes 'h'.
'art'+'h'='arth'
'ely' enclosing 'arth' is 'EARTHLY'.
(Other definitions for earthly that I've seen before include "Chance (colloquial)" , "no-hoper doesn't have" , "Relating to material things" , "Relating to material existence as distinct from a spiritual one" , "Mundane" .)