I wonder will the anemometer move, though. It's south of the midpoint of the current runway in bsal's image above. I suppose the solution is to install new independent anemometers at either end of the new runway for ATC to report local wind conditions to traffic using that runway. There already is one such anemometer at the threshold of the current runway (I posted it above). In that case the station meteorological and climatalogical wind data will remain unchanged as they can still come from the main anemometer.
I received a reply from Met Eireann regarding the email I sent about Shannon airport. I've asked permission to post the contents here and he's ok with it so here's the response
I asked as a follow up question if there are any adjustments to the raw data to take account of changes to the site location or any changes to the environment and he said