I gag on a cored root vegetable (9)
'vegetable' is the definition.
(artichoke is a kind of vegetable)
'i gag on a cored root' is the wordplay.
'gag' becomes 'choke' (synonyms).
'on' says to put letters next to each other.
'a cored root' becomes 'art' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'ichoke' put after 'art' is 'ARTICHOKE'.
(Other definitions for artichoke that I've seen before include "See 26", "Globe vegetable?", "Thistle-like plant with edible heads", "Jerusalem or globe?", "vegetable's served?".)