Luggage problem

Have you asked your hotel if they would hold your luggage?

We are staying in apartment and they can’t extend our check out time.

One of the downsides of AirBnB-type accommodations.

Consider asking them (they who own/manage your "apartment") - presumably, they live there and know their way around. If they are local residents, they'll probably know what the options are.

Also make sure you are being clear with your request: you're not asking them for a late checkout (late checkout means you get to stay in the place, and the owners' cleaners won't have access). You're just looking for a place where you can leave your bags safely for a few hours, not a late checkout. If they have no ideas, then consider asking the folks who are taking you to Galway - hopefully they're locals, too.

https://www.fodors.com/news/travel-tech/download-these-storage-apps-and-never-lug-your-luggage-around-again

There are companies that will store luggage around different cities. They use local businesses.
There are a few different ones but a quick google search came up with nannybag.com
We did use one in Dubrovnik but I don’t remember the name of the company.

You could ask at the tourist information office:
https://www.discoverireland.ie/kerry/dingle-tourist-information-centre

Assume you mean Dingle?? It is such a small town I doubt there are any left.luggage companies. The best suggestion is to ask your transport.company, perhaps they have garages or other facilities you could use for a.modest.fee. Good luck.

The Bounce app often shows hotels that will store your bags for a fee but there don't seem to be any in Dingle. You can try asking at a real hotel to see if they'll hold your bag.