The phrase "graceful exit" means leaving a situation or ending something in a calm and composed manner, without causing any disturbance or creating any problems. Full definition
The rear door openings and the position of the bucket seats make graceful exits difficult. (cars.com)
It was the victory lap of my life's drinking games — a conscious, intentional, relatively graceful exit. (mindbodygreen.com)
The best advice for these situations is to avoid excess consumption of alcohol; when you're trying to impress a client, nothing looks worse than slurring over your lunch and tripping over your napkin when you make a less than graceful exit from the table. (womenshealthandfitness.com.au)