Place a large pot or Dutch oven (6 quarts or larger) over medium heat.
When the pot is hot, add the olive oil.
Add the chopped onion, celery, and carrots. Stir and cook until the onion starts to soften, about 7-8 minutes.
Add the garlic and cook until fragrant, about 1 minute.
Add the cooked turkey and broth to the pot.
Increase heat to medium-high and bring to a boil, uncovered.
Reduce heat to low, cover, and simmer until vegetables are almost tender, about 10 minutes.
Add the pasta and simmer until cooked through, about 8-10 minutes.