Sprinkle the chuck roast generously all over with salt and pepper. Turn a 6-quart Instant Pot® to the high saute setting. Add the oil and once hot, add the beef and cook until deeply browned on both sides, about 5 minutes per side. Remove the beef from the pot, add the tomato paste and garlic and stir to combine. Add the flour and stir to make a paste. Whisk in the red wine until well combined and bring to a boil. Cook until slightly thickened, about 3 minutes.
Add the broth, potatoes, carrots, celery, rosemary, thyme, 1 tablespoon salt and a large pinch of pepper. Nestle the beef on top and place the onions on top or around the beef, wherever they fit best. Follow the manufacturer's guide for locking the lid and preparing to cook. Set to pressure cook on high for 1 hour 15 minutes.
After the pressure cook cycle is complete, follow the manufacturer's guide for quick release and wait until the quick release cycle is complete. Be careful of any remaining steam and unlock and remove the lid. Allow the beef to sit in the sauce, uncovered, for 10 minutes.
Remove the herbs from the sauce and transfer the meat to a cutting board. Slice against the grain and put on to a large rimmed serving platter. Top with the sauce and vegetables.
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