New partner for Pete in plain Welsh town (9)

I believe the answer is:

llandudno

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'welsh town' is the definition.
(I've seen this before)

I don't understand the rest of the clue.

(Other definitions for llandudno that I've seen before include "North Wales seaside resort" , "holiday destination" , "Welsh seaside resort" , "Resort of N. Wales" , "Welsh seaside town" .)

I've seen this clue in The Sunday Times and The Times.

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