Step 1
Pat chuck roast dry with a paper towel. Stir together flour salt and pepper in a small bowl. Sprinkle flour mixture all over the roast pressing lightly to ensure it sticks to the meat.
Step 2
Turn on a multi-functional pressure cooker (such as Instant Pot®) and select Saute function. Add oil. Add roast to the hot oil and cook without turning until browned about 3 minutes. Turn roast to brown each side about 3 minutes per side. Transfer roast to a plate.
Step 3
Add onion garlic and minced rosemary to the pot; cook stirring often until onion is translucent about 6 minutes. Add beef stock wine and tomato paste and simmer while scraping the browned bits of food off the bottom of the pan with a wooden spoon. Return roast to the pot along with bay leaf.
Step 4
Close and lock the lid select Meat/Stew function and set timer for 40 minutes.
Step 5
Release pressure carefully using the quick-release method according to manufacturer's instructions about 5 minutes. Unlock and remove the lid. Transfer roast to a plate and tent with aluminum foil for 15 minutes.
Step 6
Add carrots pearl onions and celery to the pot. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 4 minutes. Allow 5 to 10 minutes for pressure to build.
Step 7
Release pressure carefully using the quick-release method according to manufacturer's instructions about 5 minutes. Unlock and remove the lid.
Step 8
Slice roast against the grain or use 2 forks to pull meat into chunks. Transfer roast vegetables and sauce to a serving platter. Discard bay leaf and garnish with rosemary sprigs.