Cook the chicken shawarma and gyro meat in a skillet over medium-high heat until warmed through and slightly caramelized. Set aside and cut into bite-sized pieces.
Preheat the oven to 425°F. Place the frozen cheese pizza on a baking sheet or pizza stone.
Spread the garlic spread generously over the top of the pizza. Scatter the thinly sliced red onion evenly over the garlic spread. Arrange the sliced shawarma and gyro meat over the top.
Bake at 425°F for 12 to 15 minutes until the crust is golden and the cheese is melted and bubbly.
Let cool for about 4 minutes then top with spoonfuls of tzatziki, a drizzle of Zhoug sauce, and a generous handful of crumbled feta. Slice and serve immediately.