Knack of regularly slicing carrot (3)
I believe the answer is:
art
'knack' is the definition.
(both can mean a skill or talent)
'regularly slicing carrot' is the wordplay.
'regularly slicing' indicates alternate letters (letters sliced out at regular intervals).
The alternating letters of 'carrot' are 'ART'.
'of' is the link.
(Other definitions for art that I've seen before include "Lovely piece of work" , "A name" , "-- Garfunkel, singer" , "The works of Alma-Tadema" , "are old-fashioned" .)