Season the cod with 1/2 teaspoon salt and 1/4 teaspoon pepper. Heat the oil in a large nonstick or cast-iron skillet over medium-high heat. Cook until the undersides are golden, 3 to 5 minutes.
Flip the cod and scatter the green beans and leek around it. Add 1/4 cup water, cover, and cook until the vegetables are just tender and the fish is opaque throughout, 3 to 4 minutes.
Transfer the cod to plates. Stir the corn into the green beans, cover, and cook for 1 minute. Stir in the pesto and serve with the cod and additional pesto, if desired.