Heat olive oil in a large skillet over medium-high heat.
Add ground turkey and cook until browned, breaking it into small crumbles with a spatula for approximately 5-7 minutes.
Add diced onion and sauté for 3 minutes until translucent.
Stir in minced garlic, grated ginger, and diced water chestnuts; cook for 1 minute until fragrant.
In a small mixing bowl, whisk together soy sauce, hoisin sauce, rice vinegar, and sriracha.
Pour the sauce mixture over the turkey and stir to coat evenly; cook for an additional 2 minutes until the sauce thickens slightly.
Remove the skillet from heat and stir in the sliced green onions.
Prepare lettuce leaves by drying them thoroughly.
Spoon approximately 1/4 cup of the turkey mixture into the center of each lettuce leaf.
Garnish with shredded carrots and serve immediately.