Read Marla Apt's response:
Since there are different types of hip replacement procedures, it's helpful to learn as much as possible about the nature of your student's operation. You'll also want any information the doctor provided her about risks and range of motion limitations. Depending on the surgical approach and the location of the incision, many hip replacement patients are advised to avoid internal rotation, adduction, hip flexion (beyond 90 degrees), or even hip extension. These precautions, especially within the first year of the procedure, are aimed to keep the hip joint stable, since it's more prone to dislocation than a normal hip. For this reason, it is important to be cautious with a student who has had a hip replacement, especially if she complains of pain.
I recommend that you teach your student the variations of Supta Padangusthasana (Reclining Big Toe Pose)—such as holding her foot with a belt—so she can learn to keep her thighs rooted in the hip sockets when doing hip flexion, adduction, abduction, and external rotation.
Observe her alignment in all asanas to make sure that she's not collapsing her weight onto either hip. In the standing asanas (especially balancing poses where she stands on one leg), she can use the support of a wall to learn how to hold the thighs in the hip sockets; use the strength of her legs, buttocks, and abdominal muscles; and align her joints so that the weight of the body is distributed evenly.
Look to see that when her affected side is the front leg in the standing poses, her hip doesn't project outward, sideways, or backward. When her back leg in standing pose is the side with the hip replacement, help her so that the hip doesn't fall forward or out to the side. Also observe and correct if the opposite hip is compensating. When you observe these points, you may see that she needs the support of props for stability.