Crossword Genius

Former province of NW British India having a play with words and a poke (6)

Ross

I believe the answer is:

punjab

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'former province of nw british india' is the definition.
I can't tell whether this defines the answer.

'a play with words and a poke' is the wordplay.
'a play with words' becomes 'pun' (a pun is a form of wordplay).
'and' means one lot of letters go next to another.
'a poke' becomes 'jab' ('jab' can be a synonym of 'poke').
'pun'+'jab'='PUNJAB'

'having' acts as a link.

Can you help me to learn more?

(Other definitions for punjab that I've seen before include "Sub-continental region" , "India/Pakistan border region" , "State of northwest India" , "State of NW India, chief city Lahore" , "Province in both India and Pakistan" .)

I've seen this clue in the Sydney Morning Herald.
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