Set your Instant Pot to sauté mode, low heat. Add oil and warm over low heat until it is hot and shimmering.
Add onion and cook until it is softened and translucent. Add the minced garlic and cook for 30 seconds, stirring constantly, until the garlic is fragrant.
Add the uncooked rice to the Instant Pot. Cook, stirring constantly, until rice is coated in tomato paste and lightly browned. Add tomato paste and stir until it has coated the rice.
Add chicken broth and salt to the Instant Pot. Stir well to combine ingredients, then pour in tomato sauce and do not stir.
Secure lid on Instant Pot with vent in Sealing position. Set Instant Pot to Manual High Pressure for 7 minutes. Instant Pot will come to pressure, then 7-minute cook time will begin.
Once cook time is up, carefully Quick Release the pressure inside Instant Pot, but do not remove lid. Leave to sit, covered, for 1 to 2 minutes, then carefully remove lid and set aside.
Run spatula gently around side of Instant Pot to loosen rice. Fluff rice with a fork.