A measure of rum -- a mild sort of taste (5)
I believe the answer is:
umami
'taste' is the definition.
(I've seen this before)
'a measure of rum a mild sort' is the wordplay.
'a measure of' indicates the answer is hidden within the clue (a portion or measure of the clue).
'UMAMI' can be found hidden inside 'rum a mild sort'.
'of' is the link.
(Other definitions for umami that I've seen before include "Savoury taste sensation produced by glutamates - I, a mum (anag)" , "Fifth flavour" , "Newly discovered taste" , "Japanese word for pleasant savoury taste" , "meaty taste" .)