Pull the prime rib roast out of the refrigerator and let it come to room temperature.
Season the roast on all sides with kosher salt and coarsely ground black pepper and set aside.
Place the Instant Pot on Saute. Once the display reads HOT, add the olive oil and brown on each side.
Add the beef stock, red wine, and Worcestershire sauce to the liner of the Instant Pot. Place the trivet in the liquid.
Place the roast on the trivet. Lock the lid in place and turn the vent in the "Sealing" position. Pressure cook/Manual on HIGH pressure for 13 minutes.
Once the cook time expires, allow the pot to stay on Keep Warm for 35 minutes.
Open the pot and measure the inner temperature of the meat at the thickest part. It should register approximately 115 F.
Remove the roast to a plate to rest. Strain the liquid into a large measuring cup to remove any prime rib fat or bits and set aside.
Turn the pot on the Saute. Once the pot reads HOT, add another 2 tablespoons of olive oil to the pot. Then place the prime rib roast back and sear it until brown on all sides. Remove and place under foil to allow it to rest.
With the pot still on Saute mode, add in the strained liquid until hot. Remove and place in a serving dish and serve alongside the roast.