Remove the turkey from the fridge. Do not rinse the brine off of the turkey. Preheat the Traeger to 225°F.
While the smoker heats up, stuff the cavity of the turkey with the onion and orange wedges. Tuck the wings behind the back of the turkey and tie the ankles together with baker's twine (this step is optional, but it makes the turkey look nicer and helps it cook more evenly).
Stick a leave-in thermometer into the thickest part of the turkey breast.
Place the turkey on the smoker and close the lid (keep the turkey in the roasting pan).
Place 6 tablespoons of butter in a microwavable bowl. Add the reserved herb/brine mixture and melt it in the microwave.
After the turkey cooks for 1 hour, increase the heat on the Traeger to 350°F. Baste the turkey with the melted butter mixture and close the lid.
Continue basting the turkey every 30 to 40 minutes until the temperature on the meat thermometer reaches 160°F to 165°F. This usually takes 2-1/2 to 3-1/2 hours for a 14 to 16-pound turkey. The time will vary, so make sure you cook the bird until the internal temperature reaches 160°F to 165°F.
Remove the turkey from the Traeger smoker, cover with foil, and let rest for 20 minutes.
Slice and serve!