In recession manage hospital for period (5)
I believe the answer is:
epoch
'for period' is the definition.
(epoch is a kind of period)
'in recession manage hospital' is the wordplay.
'in recession' says the letters should be written in reverse (letters recede or go back).
'manage' becomes 'cope' (manage can mean to cope or do well).
'hospital' becomes 'h' (abbreviation for hospital on maps).
'cope' written backwards gives 'epoc'.
'epoc'+'h'='EPOCH'
(Other definitions for epoch that I've seen before include "Period, era" , "Historical era" , "Making this date" , "Aeon" , "Historical period" .)