Pat the chicken with paper towels all over so it is dry, gently separate the skin from the breast meat by sliding your hand under the skin from the bottom of the breast, set aside.
In a medium-sized bowl, stir together the salt, pepper, 2 cloves of the garlic, minced, the thyme, rosemary, and parsley. Place half of the butter mixture under the skin and smooth it out so it covers the breast meat evenly, set aside.
Add the trivet to the instant pot, pour the chicken stock in the bottom. Add the chicken breast side up into the pot.
Cut the remaining head of garlic in half lengthwise so all of the cloves are exposed, stuff the chicken with the two halves. Smooth the remaining butter mixture all over the top of the chicken.
Add the lid, pressure cook, on high for 6 minutes per pound, with a 15-minute natural release. Take the chicken out of the pot and add it to an oven-safe baking dish, broil on high until golden brown. Make sure to watch this closely as it is easy to burn.
To make the gravy, pour out the chicken drippings from the bottom of the pot. Skim off 3 tablespoons of the fat from the drippings. Wipe out the bottom of the pot so there is no leftover residue. Place the pot back into the appliance and place it on the high saute setting. Once hot, add the 3 tablespoons of fat and whisk in the flour, stirring constantly. Cook for two minutes.
Whisk in 3 cups of the drippings stirring constantly, if your chicken did not make 3 cups, add more chicken stock up to 3 cups. Let come to a simmer and thicken for about 5 minutes. Taste and adjust seasoning if necessary. Serve the chicken with the gravy and enjoy!