Allow the hospital to treat Gary for lassitude (8)

I believe the answer is:

lethargy

'for lassitude' is the definition.
(synonyms)

'allow the hospital to treat gary' is the wordplay.
'allow' becomes 'let' (synonyms).
'the hospital' becomes 'h' (abbreviation for hospital on maps).
'to treat' indicates anagramming the letters.
'gary' with letters rearranged gives 'argy'.
'let'+'h'+'argy'='LETHARGY'

(Other definitions for lethargy that I've seen before include "Unnatural drowsiness" , "'Lassitude, langour (8)'" , "Lack of energy and enthusiasm" , "Extreme lack of energy, listlessness" , "Lassitude, languor" .)

I've seen this clue in the Evening Standard.

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