Short cut on course of healing (4)
I believe the answer is:
cure
'course of healing' is the definition.
(course of medicine to heal something)
'short cut on' is the wordplay.
'short' means to remove the last letter.
'on' becomes 're' ('on' can be mean 'with reference to').
'cut' with its final letter removed is 'cu'.
'cu'+'re'='CURE'
(Other definitions for cure that I've seen before include "Remedy, therapy" , "Restore to health or preserve with salt" , "Make healthy, preserve" , "Heal or pickle" , "Heal or preserve" .)