In Ireland brown bears were plentiful in past centuries. Pre-ice-age brown bears in Ireland lived between 38,000 and 43,000 years ago. Descendants of these are still found in today's bears of eastern Europe. Brown bears from 3,000 to 5,000 years ago have descendants in western Europe.The now extinct Irish brown bears we are interested in lived about 10,000 to 38,000 years go.
The National Museum of Ireland has bones recovered from the Poll na mBear cave in 1997. When DNA testing was done on these bones, the results showed that these bears are the female ancestors of present day polar bears. Until now the closest DNA match for polar bears was brown bears living on the Alaskan islands.
The theory is that at some point during the last major Ice Age the polar bears of that time and the Irish brown bears crossed paths. Cross-breeding or "hybridization" often occurs between related but distinct species at times of environmental stress. The offspring of ancient polar bears and Irish brown bears have evolved into the polar bears of today.
During this study DNA from more than 240 bears, both living and dead, were studied. These were from bears all over the world.
So all polar bears have an Irish ancestor. If you would like to see more about this I have provided you with a couple of links below.