Set your Instant Pot to the sauté function. Add olive oil, onion, green bell pepper, and celery. Sauté for about 5 minutes until the vegetables are softened. Stir in garlic and cook for an additional minute until fragrant.
Add the sliced andouille sausage to the pot and cook for about 3 minutes, stirring occasionally.
Stir in the diced tomatoes (with juice), rice, chicken broth, Cajun seasoning, thyme, bay leaf, salt, and pepper. Mix well to combine all ingredients.
Close the lid of the Instant Pot, ensuring the valve is set to sealing. Select the manual or pressure cook function and set the timer for 8 minutes.
Once the cooking time is complete, allow for a natural pressure release for 5 minutes, then carefully switch the valve to venting to release any remaining pressure.
Open the lid and stir in the shrimp. Close the lid again and let it sit for 5 minutes to allow the shrimp to cook through.
Remove the bay leaf and fluff the jambalaya with a fork. Garnish with sliced green onions and chopped parsley before serving.