Heat peanut oil in a large saucepan over medium-high heat. Add onion and red bell pepper; saute until softened, about 4 minutes. Reduce heat to medium. Add ginger and garlic; cook and stir until fragrant, 1 to 2 minutes. Stir in red chile paste and coconut milk. Add the clams and simmer until flavors combine, 3 to 5 minutes. If curry appears too thick, stir in chicken broth.
Finely grate zest from the lime. Stir half of the zest into the curry along with fish sauce and brown sugar. Squeeze some lime juice into the curry. Stir in half of the basil and shrimp; simmer curry until shrimp are opaque and cooked through, 5 to 10 minutes. Thin the curry with more chicken broth if needed.
Scoop clams out of the curry, draining their juice back into the saucepan, and discard. Mix in remaining lime zest and basil before serving.