Sprinkle the chicken pieces with 1/2 teaspoon salt and 1/2 teaspoon pepper.
Heat a large skillet or pot over medium heat and add 2 tablespoons coconut oil. Add the chicken and cook, stirring occasionally, until browned and cooked through, about 6–8 minutes. Transfer the chicken to a plate.
If needed, add a little more coconut oil to the skillet. Add the sliced leeks and cook until softened, about 3–4 minutes.
Stir in the minced garlic, grated ginger, and red curry paste and cook for 1 minute until fragrant.
Add the halved snow peas and the cooked chicken back to the skillet and stir to combine. Cook for about 5 minutes.
Increase heat to medium-high and pour in the pomegranate juice, scraping the bottom of the pan; cook 1–2 minutes.
Add the 14-ounce can of coconut milk, bring to a boil, then reduce to a simmer. Stir in the lime juice and grated zest and simmer 10 minutes. Taste and adjust seasoning if needed. Garnish with chopped cilantro and 1/3 cup pomegranate arils before serving.
Meanwhile, heat a saucepan over medium-high and combine the jasmine rice, 1 1/2 cups light canned coconut milk, 1/2 cup coconut water, and 1/4 teaspoon salt. Stir and bring to a boil.
Reduce heat to low, cover, and cook the rice 15–18 minutes until liquid is absorbed. Fluff with a fork, then stir in 1 tablespoon coconut oil and the remaining 1/3 cup pomegranate arils.
