Staff officer's supporters were seated round hospital (5,3)
I believe the answer is:
brass hat
'staff officer's' is the definition.
(brass hat can informally mean a military officer)
'supporters were seated round hospital' is the wordplay.
'supporters' becomes 'bras' (a bra gives support to breasts).
'were seated' becomes 'sat' ('they were seated' means 'they sat').
'round' indicates putting letters inside.
'hospital' becomes 'H' (abbreviation for hospital).
'sat' placed around 'h' is 'shat'.
'bras'+'shat'='BRASS HAT'
(Other definitions for brass hat that I've seen before include "Top-ranking officer" , "High-ranking official or officer with metal headgear?" , "High-ranking officer in armed forces (colloq.)" , "official of the first rank" , "general? Possibly" .)