Impoverished country lacking a good part of hospital (8)
I believe the answer is:
indigent
'impoverished' is the definition.
('indigent' can be a synonym of 'impoverished')
'country lacking a good part of hospital' is the wordplay.
'country' becomes 'india' (India is an example).
'lacking' indicates named letters should be taken away.
'good part of hospital' becomes 'gent' (I am not sure about this - if you are sure you should believe this answer much more).
'india' with 'a' taken away is 'indi'.
'indi'+'gent'='INDIGENT'
Can you help me to learn more?
(Other definitions for indigent that I've seen before include "Poor and needy" , "poor fellow" , "Impoverished -- ending it (anag)" , "Poor enough to need help from others" , "Impoverished, destitute" .)