Getting better in hospital somewhere in London (7)
I believe the answer is:
healing
'getting better' is the definition.
('heal' can be a synonym of 'get better')
'hospital somewhere in london' is the wordplay.
'hospital' becomes 'h'.
'somewhere in london' becomes 'ealing' (I've seen this in other clues).
'h'+'ealing'='HEALING'
'in' is the link.
(Other definitions for healing that I've seen before include "Restoring to health" , "Recovering, becoming healthy" , "Getting better" , "Curative" , "Mending" .)