Cook the pasta according to the package directions. Drain and rinse well.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the garlic, salt, and pepper. Cook until the garlic is fragrant, about 1 minute.
Add the asparagus and peas. Cook for 5 minutes, until starting to soften.
Turn off the heat and add the cooked pasta to the pan, along with the arugula, lemon juice and zest, feta cheese, parsley, and chives. Serve immediately.