Turn on a multi-functional pressure cooker (such as an Instant Pot®) and select 'Saute' function. Heat olive oil and add onion; cook until softened, about 7 minutes. Add garlic and cook for 1 minute more.
Combine tomatoes, vegetable stock, basil, salt, black pepper and Italian herb seasoning in the pot. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid.