Bring a large pot of salted water to a boil. Add the potatoes and simmer for 12 to 15 minutes until just tender. Drain and allow to cool for 5 to 8 minutes.
Grate the cucumber and squeeze out the moisture.
In a large bowl, combine the Greek yogurt, grated cucumber, lemon juice, olive oil, salt, pepper, and minced garlic. Stir well until combined.
Add the cooled potatoes to the bowl along with the quartered cucumbers, fresh mint, dill, chives, lemon zest, Kalamata olives, feta cheese and stir to mix.