Pursue legal proceedings involving hospital (5)
I believe the answer is:
chase
'pursue' is the definition.
(chasing is a kind of pursuing)
'legal proceedings involving hospital' is the wordplay.
'legal proceedings' becomes 'case'.
'involving' indicates putting letters inside.
'hospital' becomes 'h'.
'case' placed around 'h' is 'CHASE'.
(Other definitions for chase that I've seen before include "Pursuit" , "Engrave - hunt - pursue" , "Pursue, run after" , "grave, as before?" , "trail" .)