I belive that the Celts were a people who migrated in to Europe, from somewhere in Eurasia…just whne , I don’t know. By the the time of Julius Caesar, the Celts were dominant in Gaul, England and ireland. But what became of the earleir inhabitants of ireland? Were they driven out, or did the intermarry and merge with the Celts?
They hid in the hills. 
I honestly broke into laughter at this. Darned tuath-ing* they did!
Pronounced “tooting”, as in Tuatha de Danaan (TOOT-uh day DAN-yan).
On a slightly more serious note though, and remember I’m not expert, Ireland saw large structures being built prior to the Celts. This along with cereal crops suggest a relatively settled number of people. So I’d imagine you’d see a progressive replacement of “native” power centers with newer iron age one. Essentially a fading of the prior inhabitants along with, no doubt, clearing of fertile farming areas.
I’ve always known the pronunciation to be “too-ah” not “TOOT-uh”.
There was also the Beaker People.
The Celts probably arrived in small numbers, but had prestige due to military or technological skills, so the locals eventually adopted Celtic language, religion, etc.
I once read that a red-haired gene still almost unique to Ireland was present there many thousands of years ago (long before Celt arrival). Sorry, no cite for this; nor any opinion about its scientific validity.
This New York Times article cites genetic studies suggesting that
Of course, there’s more than one genetic opinion. Look to language studies, as well.
Bob Quinn’s The Atlantean Irish: Ireland’s Oriental & Maritime Heritage gives a non-academic’s view of Irish origins & history. (The book has nothing to do with Atlantis!) Sir Barry Cunliffe, professor emeritus of European archaeology at Oxford, wrote the preface to the latest edition. A well-known authority in Celtic Studies, his own Facing the Ocean: The Atlantic & Its Peoples gives the very big picture of European prehistory. In it, he sees the Celtic languages as descendants of a lingua franca used in the peninsulas & islands connected by the Atlantic. The concept of A Celtic People thundering across Europe is a bit outdated.
Ouch! That book is OOP & hideously expensive. Check out Cunliffe’s Europe Between the Oceans for another look at early days in Europe–quite free from Celtic Mists…
Yes, as said above, the “Celts” probably arrived when the indigenous inhabitants switched to speaking proto-Insular-Celtic (and its Indo-European cultural heritage). There’s no evidence of any large migration; any population movment was probably a smaller elite, military or mercantile or both. Latest theories suggest via Spain, as indeed the medieval Irish said, though there’s still support for the idea of colonization from Gaul.
Tuath is “TOO-ath” in Old Irish, “TOO-ah” in modern. Tuatha is “TOO-a-tha” > “TOO-uh-huh.” Punsters go by their own rules.