Preheat the Traeger to 375°F.
Remove the chicken from its packaging and remove any giblets from the cavity. Pat the chicken very dry with paper towels.
In a small bowl, combine the softened butter, grated garlic, rosemary, thyme, lemon zest, kosher salt and black pepper.
Carefully loosen the skin over the chicken breasts using your fingers. Rub some of the garlic herb butter underneath the skin, then spread the remaining butter all over the outside of the chicken.
Place the lemon halves and a few sprigs of fresh rosemary and thyme inside the cavity. Tie the legs together with kitchen twine if desired.
Add the potatoes, carrots, onion and halved garlic head to a large rimmed sheet pan. Drizzle with olive oil, season with salt and pepper and toss until evenly coated.
Make a space in the center of the sheet pan and place the chicken breast-side up in the middle. Arrange the vegetables around the chicken in a mostly even layer.
Place the entire sheet pan directly onto the preheated Traeger.
Cook for approximately 1 hour 15 minutes to 1 hour 45 minutes, tossing the vegetables carefully once or twice during cooking. Cooking time will vary depending on the size of your chicken and your grill.
Begin checking the chicken with an instant-read thermometer. The thickest part of the breast should reach 165°F, while the thigh should be around 170–175°F.
If the chicken reaches temperature before the vegetables are as golden and tender as you’d like, transfer the chicken to a cutting board to rest and return the sheet pan of vegetables to the Traeger for another 10–15 minutes.
Allow the chicken to rest for at least 10–15 minutes before carving.
Transfer the chicken to a large serving platter and arrange the roasted potatoes, carrots, onions and garlic around it. Spoon some of the buttery pan juices over everything and finish with fresh herbs and lemon wedges.