Welshman left house in Ireland (4)

I believe the answer is:

dail

I'm a little stuck... Click here to teach me more about this clue!

'house in ireland' is the definition.
'Dail' can be an answer for 'house' (Dail is an example). I am not sure about the 'in ireland' bit.

'welshman left' is the wordplay.
'welshman' becomes 'Dai' (Welsh name).
'left' becomes 'l' (common abbreviation).
'dai'+'l'='DAIL'

Can you help me to learn more?

(Other definitions for dail that I've seen before include "Paper" , "Lower house of the Irish legislature" , "Dublin house" , "Himalayan kingdom" , "Lower house of the Irish parliament" .)

I've seen this clue in The Independent.

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