Some pros look more graceful than others, though all professionals look pretty damn good.  Is it due to years of practice, genetics, athleticism?  Who knows, but let me share what I learned that may have helped along the way.

Gracefulness how-to.  Like dancers, this is performed in front of a mirror so you get feedback in order to reinforce the body movement required.

Objective: to reinforce weight shift for the bow and toss arm lift, 1-2-3 Go!; to eliminate your self-consciousness; to familiarize yourself with how your body's working; to recognize the rhythm, speed, timing, and spacing of these elements.

Method: no racket needed.  Stand in front of a mirror and while looking directly at the mirror begin to move your waistline to reflect the archer's bow while dropping the arms together and raising them together for their different objectives.  The toss arm is as straight up as it can be, the racket arm up half-way and bent, the hand up to simulate holding a racket.  Look at yourself in the mirror while doing this to reinforce the bowing of the body, the upward arm.  Return to a starting position and repeat, many times.  Practice as often as possible, forever.

The special tip to add here is dancers wear either very tight clothing or clothing that reveals more than it conceals in order to get the feedback they want from the mirror and their body.  Tennis players need to practice their serve motion's gracefulness in exactly the same manner dancers practice their moves.  The idea is to both explode your self-consciousness and notice how the individual parts of your body move (groin, hips, toss arm), when each moves, and by how much during the weight shift and bow.  Once imprinted the speed and sequence to how the groin moves, the hip sways, and the arms lift can you transfer this when on the court and think only about hitting the ball.

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