Heat the oil in a large nonstick or cast-iron skillet over medium-high heat.
Season the cod with ½ teaspoon salt and ¼ teaspoon pepper. Cook until the undersides are golden, 3 to 5 minutes.
Flip the cod and scatter the green beans and leek around it.
Add ¼ 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 beans, cover, and cook for 1 minute. Stir in the pesto. Serve with the cod and additional pesto, if desired.