Thank you for consulting.
Calf pain while running and subsiding with rest can be due to muscle fatigue. Most commonly seen in athletes, this is usually caused by either over stressing your with excessive training activities or faulty technique in physical exercise and training. Your calf muscles can become weak with loss of endurance due to these reasons over time and this can present as calf pain.
Although, it is important to exclude other important causes of calf pain like sciatica, obstruction of blood supply to calf muscles due to any reason.
Check with your physical trainer regarding modifying your training schedules and improving your technique, so that you are not overstressing your calf muscles. Consult a sports medicine specialist or physiotherapist, who can help you with exercise routines which can improve endurance power of your calf muscles. Proper diet schedule with protein rich foods is also necessary for improving muscle strength.
Hope this helps. Do get back to me with any further questions.