One of the first skills I teach my horses under saddle is how to flex left and right. This movement is used to implement a safety stop if my horse gets stressed or overwhelmed, and also to teach suppleness through the neck and ribcage. The horse should remain still and relaxed through this movement and the contact should be released as soon as the horse begins to let go through their jaw.
For some horses who are struggling with this movement, don't wait for them to fully flex on their first attempt. Instead reward any little try and find a good place to finish. It doesn't matter if it takes several sessions to achieve full suppleness. Bear in mind, however, that most suppleness issues are related to sore issues within the horses body. Having your horse checked over by a reputable body worker is encouraged to ensure that your horse is able to use their body correctly without discomfort of any kind. You may also need to have your horses teeth checked to make sure there are no issues present.
To learn how to position your body to flex your horse left and right, check out my "Correct Position for Flexing Left and Right" video, in my CORRECT POSITION FOR LATERAL MOVEMENTS video series.