A very small amount of sense (5)
I believe the answer is:
touch
This clue is a double definition.
'a very small amount' is the first definition.
(a touch of something is a small amount of it)
'sense' is the second definition.
(I know that touch is a sense)
'of' is the link.
(Other definitions for touch that I've seen before include "Deal with" , "Distinctive detail" , "off pitch" , "Manner of playing piano, say" , "Affect; a small amount" .)