Prepare round steak by trimming off any extra fat from the edges and slicing the beef into one-inch-thick steaks.
Combine the flour, salt, and pepper in a gallon-sized bag. Toss the round steaks in the flour to coat both sides.
Set the Instant Pot to sauté mode and add the olive oil.
Working in batches, place the steaks in the oil and brown both sides, then remove and set aside.
Add the onion, celery, carrot, and garlic to the pot. Stir and sauté until the onion is translucent and the carrots are tender.
Turn off the Instant Pot and add the beef broth. Use a wooden spoon to scrape the bottom of the pot.
Add the Worcestershire sauce, Italian seasoning, diced tomatoes, and tomato paste. Stir to mix.
Place the steaks back in the pot and press into the sauce.
Cover with the lid, lock it, and turn the valve to the sealing position. Cook on high pressure for 25 minutes, then do a natural release.
When all the pressure has been released, remove the lid and take out the steaks.
If the sauce has not thickened, add the cornstarch slurry to the pot. Stir to mix and sauté the sauce for 5 minutes, until thickened