Aside from world championship competitions, in 1990 she took first place at both the Biel Women's Open and Geneva (IM), then followed up by winning the Doeberl Cup in Canberra, Australia in 1991,[1] becoming the first woman to do so.

In the 1990s, she participated in the Veterans vs Ladies dance-themed tournaments where she defeated Borislav Ivkov, Vlastimil Hort, Vasily Smyslov and Mark Taimanov.

Journalist John Saunders describes Arakhamia-Grant as the ideal role model: "her charming and dignified manner belies a tough, determined fighter at the board.

At the 2008 EU Individual Open Chess Championship in Liverpool, she shared the highest scoring woman prize with Jovanka Houska and Yelena Dembo.

Having additionally met the 2500 Elo rating requirement in the January 2009 FIDE list, she was awarded the title in March 2009, making her Scotland's sixth grandmaster.

In league chess, Arakhamia-Grant has played for OSC Baden-Baden in the Women's Bundesliga and for Georgian team Interplast Tbilisi in the European Club Cup.