It may take some time, but lots of transitions and making sure you are pushing your horse up into the bridle, asking him to work correctly though his back rather than creating a false outline by using your hands to pull his neck in. Walk to canter and rein back/halt to trot/canter are especially useful:)
What you are looking for is impulsion. Impulsion is one of the final steps of the Training Scales. If you research the scales, there's loads of resources. Before impulsion, you need rhythm, relaxation and connections (acceptance of the aids). Impulsion and straightness are quite interchangeable and one horse will not achieve impulsion without straightness, and another will not achieve straightness without impulsion.