If a Non-Jew calls you from a time zone where it is already Shabbos but in your location Shabbos has not yet arrived, may you speak to him? Is this considered Amira L’Akum (telling a Non-Jew to do Milacha), for causing a Non-Jew to do Melacha for you
The Chelkas Yaakov (OC 87) says the Rema paskens (YD 297) that Amira L’Akum is forbidden for any issur and not only Issurei Shabbos. For example you cannot ask a Non-Jew to sterilize your animal. However it is only forbidden when the action is assur for you, the Jew, as well. In this case, right now where you are standing Shabbos has not yet arrived. By talking to a Non-Jew in a different time zone you are not imposing on him something that you yourself are prohibited from doing. The fact that the Non-Jew is in a city where Shabbos has already begun for the Jews of that city, is totally irrelevant.
He does add one caveat however. If it is public knowledge that the Non-Jew is running the business of a Jew who lives abroad, it is forbidden for the Non-Jew to operate that business after Shabbos starts in that location in accordance with the Shulchan Aruch (OC 263).