The Gaelic word for king is rìgh and is pronounced ree. There are a couple of variants for the Gaelic word for queen. The most common, especially in official Gaelic, is ban-rìgh, which is simply the word for king with the feminine prefix bolted on to the front. But one will also encounter banrighinn, which comes from merging the “official” word with an older Gaelic word for queen, rìgain.
By extension, the Gaelic word for kingdom is rìoghachd, and the UK is Rìoghachd Aonaichte. In colloquial Gaelic, rìoghachd is often used for country or nation whether the land has a monarch or not. Many will refer to Alba (Scotland) as a rìoghachd in its right, whether they believe in Scottish independence or not. The Gaelic word for republic is poblacht and a president will be called ceannsuidhe, literally “sitting head”.