Final answer:
The nurse's best action is to loosen the dressing and elevate the extremity to the level of the heart.
Step-by-step explanation:
The nurse's best action when caring for a client who develops compartment syndrome after an embolectomy for peripheral arterial disease is to loosen the dressing and elevate the extremity to the level of the heart. Compartment syndrome occurs when there is increased pressure within a muscle compartment, leading to compression of blood vessels and nerves. Loosening the dressing and elevating the extremity helps to relieve the pressure and improve blood flow.