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'm not certain of 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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