The most common IT band stretch (crossing one leg behind the other and driving the hip out to the side) is more of a tensor fascia latae stretch, which could be helpful if the TFL is tight.

What is your IT band? The iliotibial band (ITB), or ... ‘At the top of the leg, your glutes and tensor fascia latae muscles (TFL) insert into it and are able to control some of the tension ...

The clamshell exercise is known to target key muscles such as the gluteus medius and minimus, along with the tensor fasciae ...

The iliotibial band is a functional tendon in that it is dynamized by the tensor fascia, a muscle that is a hip flexor and rotator that helps advance the limb as well as stabilizing the knee.