Short-lived artist isn't running around hospital department (9)
I believe the answer is:
transient
'short-lived' is the definition.
(I know that short-lived can be written as transient)
'artist isn't running around hospital department' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'running' is an anagram indicator (the letters run around to different places).
'around' means one lot of letters goes inside another.
'hospital department' becomes 'ENT' (Ear, Nose and Throat department).
'isnt' anagrammed gives 'tnsi'.
'ra' put into 'tnsi' is 'transi'.
'transi'+'ent'='TRANSIENT'
(Other definitions for transient that I've seen before include "Passing, short-lived" , "Temporary worker" , "Fleeting" , "Lasting little time" , "gone in a trice!" .)