“Can you have him call me when he gets in?”
You call a client's office. The client isn't there, so his assistant answers. You want to talk to the client, so you say this to the assistant.
Can you have him call me when he gets in?
When you are in charge of someone, like an employee, you can "have them" do things for you. For example:
I'll have my assistant send you those documents later today.
Why don't we have the waiter bring us the check now so that we can leave quickly?
You also use this expression to ask someone to pass a message like this:
Can you have her call me?
Talk about arriving at work with the phrase "get in":
What time do you usually get in?
I got in a little late this morning.
You can also add "to work":
What time do you usually get in to work?