To prevent the development of an external rotation deformity of the hip in a client who must remain in bed for any period of time, the most appropriate nursing action would be to use which equipment

A trochanter roll  

Explanation:

A trochanter roll often refers to the cylindrical prop such as a foam roll, rolled up towel, cylindrical pillow that is usually positioned around the thigh or hip region of the person so that they can perform extra comfort to the person lying on the bed.

This is done so that any extra deformities of the hip does not takes place due to remaining on the bed for a long time.

In this case it is place in he chest of ilium to the mid thigh region to prevent external deformities.