Wash the zucchini and cut it into uniform slices. Make sure the large shrimp are well dried with a piece of paper towel, so they cook better later. Set the fresh pesto and olive oil within reach.
Heat half of the olive oil in a grill pan over medium-high heat. Grill the zucchini slices on both sides until they are soft and have clear grill marks. Remove the vegetables from the pan and set them aside on a plate for now. Then pour the remaining olive oil into the hot pan and cook the shrimp for three to four minutes on all sides until pink and fully cooked.
Add the grilled zucchini slices back to the pan with the cooked shrimp. Add the tablespoon of fresh pesto and stir everything well together. Warm everything through for about one minute more on low heat, so the flavors mix well and the pesto is evenly distributed over the ingredients.
Remove the pan from the heat. Divide the warm mixture of shrimp and zucchini directly onto the plates and serve the dish immediately.