Crush the whole cloves lightly with the side of a knife to release their aroma, then combine with the citrus zests, olive oil, salt, and pepper in a mixing bowl to create the marinade.
Use paper towels to pat the chicken drumsticks dry; this helps achieve a crispy skin once grilled.
Submerge the drumsticks in the marinade, turning them to coat evenly, then cover and refrigerate for at least 30 minutes to let the flavors penetrate the meat.
Preheat your grill or grill pan over medium-high heat until hot, and brush the grates lightly with oil to prevent sticking.
Remove the chicken from the marinade, allowing excess to drip off; place the drumsticks on the grill, skin side down, and listen for the sizzling sound as they hit the hot surface.
Grill the drumsticks for about 5-7 minutes per side, turning occasionally until the skin is golden brown and crispy, and the internal temperature reaches 165°F (74°C).
As the chicken cooks, the marinade should sizzle and caramelize slightly, creating a smoky aroma that infuses every bite.
Once cooked through and evenly charred, transfer the drumsticks to a platter and let rest for a few minutes to allow juices to redistribute.
Serve the grilled chicken drumsticks hot, with crispy skin and tender insides, accompanied by your favorite sides.