Short Answer: To carry out your instructions. The person will do something exactly as you said it. Long Answer: To execute someone's call means to execute or to carry out the orders of the person or the organization exactly as stated. You could also say: KPD will also assist you as AVP and will help you with the locals by following your directions(instructions, orders, etc). I hope this helps you out !

It is fair to say that the term "execute your call" is almost certainly not written by a native speaker.

execution = the carrying out of a sentence of death on a condemned person. So it could be to give a death sentence to the phone call, in other words cut the call. I am not sure, I am just guessing.