Stir together the thyme, sage, salt, and pepper in a small bowl.
Set the Instant Pot to Saute, and pour the olive oil into the pot. Add the onion and saute for 2 minutes, stirring constantly. Turn off the heat, then add the garlic, chicken broth, potatoes, carrots, green beans, and half the seasoning mixture (thyme, sage, salt, and pepper) to the pot. Stir, then place the chicken on top, and sprinkle it with the other half of the seasoning mixture. Cover the pot, turn the knob to Sealing, and set the pot on manual high pressure for 10 minutes.
After the 10 minute cook time, let the pressure release naturally for 5 minutes, then turn the knob to Venting to release the remaining pressure. Remove the cover and check the chicken with a meat thermometer to be sure it's reached 165 degrees.
Turn off the pot. Remove the chicken from the pot and place it on a cutting board. Remove the vegetables to a large bowl using a slotted spoon. Chop the chicken into bite-sized pieces.
In a small bowl, stir together the arrowroot starch and water. Set the Instant Pot to Saute. Slowly whisk the arrowroot mixture into the broth. Whisk for a couple minutes, until thickened.
Return the chopped chicken and vegetables to the pot and stir. Garnish with fresh herbs if desired, and serve warm.