Man better after hospital admission (4)
I believe the answer is:
chap
'man' is the definition.
(term for a man)
'better after hospital admission' is the wordplay.
I cannot quite see how this works, but
'hospital' could be 'h' (abbreviation for hospital on maps) and 'h' is found in the answer.
'better' could be 'cap' (both can mean to beat somebody else's attempt) and 'cap' is located in the leftover letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for chap that I've seen before include "Bloke, fellow" , "Man; (of skin) turn sore" , "Cracked patch (of skin) - gentleman" , "Become raw from cold - fellow" , "(Of skin) become sore" .)