Set the Instant Pot to sauté mode and add olive oil. Sear beef on all sides (in batches if needed). Remove and set aside.
Add onion, celery, and garlic. Sauté for 2-3 minutes until fragrant. Stir in tomato paste, Worcestershire sauce, thyme, salt, and pepper.
Pour in small amount of beef broth (about 1/2 cup) and scrape up any browned bits from the bottom of the pot. This prevents a burn notice.
Return the beef to the pot along with carrots, green beans, bay leaf, and the rest of the broth. Stir to combine.
Seal the lid and cook on high pressure for 35 minutes. Allow natural release for 10 minutes, then quick release any remaining pressure.
Turn on the sauté mode, stir in the arrowroot slurry, and cook for 2-3 minutes until the stew thickens.
Remove the bay leaf, taste, and adjust the seasoning if needed.