Heat the olive oil in a large pot over medium-high heat and brown the ground turkey in it for 3-4 minutes. Add the onion, the pepper; cook for a few minutes, until the onion is translucent.
Add chicken broth, tarragon, carrots and potatoes; bring to a boil then lower to medium-low heat and simmer until the potatoes are tender, about 20 minutes, stirring occasionally. Season with salt and pepper, then add the barley; cook until barley is tender, about 15 minutes.