Acknowledge hospital is having trouble (4)
I believe the answer is:
hail
'acknowledge' is the definition.
(thesaurus)
'hospital is having trouble' is the wordplay.
'hospital' becomes 'h'.
'is having' says to put letters next to each other.
'trouble' becomes 'ail' ('ail' can be a synonym of 'trouble'**).
'h'+'ail'='HAIL'
(Other definitions for hail that I've seen before include "Greet - bad weather" , "volley" , "wintry weather" , "Fall of ice" , "arrival from the heavens" .)