Season the shrimp with salt and pepper, then add butter to the Instant Pot. Using the display panel select the SAUTE function.
When butter melts, add shrimp and cook, tossing occasionally, until opaque throughout, 3 - 4 minutes. Transfer shrimp to a shallow dish and cover loosely with foil.
Add olive oil to the pot. When oil is hot, add onion, celery, and carrots to the pot and saute until softened, 3 - 4 minutes. Add garlic and cook for 1 - 2 minutes more.
Add brandy to the pot and cook for 30 seconds, then add broth to the pot and deglaze by using a wooden spoon to scrape the brown bits from the bottom of the pot.
Add tomatoes to the pot and stir to combine.
Turn the pot off by selecting CANCEL, then secure the lid, making sure the vent is closed.
Using the display panel select the MANUAL or PRESSURE COOK function*. Use the +/- keys and program the Instant Pot for 8 minutes.
When the time is up, quick-release the pressure, then use an immersion blender to puree the soup.
Stir in heavy cream, adjust seasonings, then ladle the soup into bowls and top with the shrimp and chives.
Notes
*The MANUAL and PRESSURE COOK buttons are interchangeable.