Stretching exercises targeting the glute medius muscle can help alleviate tightness and improve hip mobility, making them beneficial for individuals experiencing discomfort on the outside of the hip. 

Tightness on the outside of your hip could signal an issue with the glute medius muscle, which is important for hip stability and strength. This muscle absorbs pressure during single-leg motions such as sprinting or stair climbing, and it can become tight and uncomfortable when weary. Several stretches are recommended by physical therapists to relieve glute medius stress. These include the sitting Figure 4 stretch, the elevated pigeon stretch, the posterior capsule stretch, the glute medius foam roll, and the sitting glute medius stretch. These stretches target various parts of the glute medius and can aid in stress relief and mobility. These stretches might help anyone experiencing hip tightness recover normal movement. 

Source: https://www.menshealth.com/fitness/a43827721/gluteus-medius-stretch/