She joined the Tbilisi-based human rights advocacy organization Article 42 of the Constitution in 2003.
[1] In 2012, she joined the new opposition party Georgian Dream - Democratic Georgia (GDDG) founded by the tycoon Bidzina Ivanishvili.
On April 21, 2012, Kobakhidze became the GDDG's temporary chairperson as Ivanishvili was not allowed to lead the political party due to his being stripped of Georgian citizenship.
[3] During the 2016 Georgian parliamentary election, Kobakhidze was 11th on the GDDG's proportional list.
The GDDG got 44 mandates with its proportional list, resulting in Kobakhidze becoming an MP, serving her 2nd term.