State: “Poke after joke” (6)
I believe the answer is:
punjab
'state' is the definition.
(I've seen this before)
'poke after joke' is the wordplay.
'poke' becomes 'jab' (synonyms).
'after' says to put letters next to each other.
'joke' becomes 'pun' (punning is a kind of joking).
'jab' after 'pun' is 'PUNJAB'.
(Other definitions for punjab that I've seen before include "Province in both India and Pakistan" , "State of northwest India" , "Province of Pakistan, capital Lahore" , "Asian region" , "State of NW India, chief city Lahore" .)