When Mordechai says rescue will come from “another place,” he means that rescue will come from H-Shem. He can be confident about this because the Yerushalmi (Simchos 8) quotes a verse (Vayikra 26:44) in saying that H-Shem promised that He would always rescue the Jews.
Therefore, the Kissey Shlomo and Dina Pishra write that H-Shem will find a way to rescue His people.
According to the Me’am Loez, one of the methods H-Shem could use in stopping Achashverosh is killing him through a rival nation. Mordechai is pointing out to Esther that, as queen, this method would be precarious for her; historically, fates worse than death can await a conquered queen.
The Chasam Sofer points out that Makom “place” can mean H-Shem, as we say in the phrase we use to comfort mourners.
R’ Moshe Meir Weiss points out that this is another example of Megillas Esther performing mental acrobatics to avoid using H-Shem’s Name.
R’ Shmuel Houminer asks why Mordechai is pushing Esther to perform this action. Did he not have faith in H-Shem. He answers that a person is required to have faith in H-Shem, but not trust specifically in his own method of achieving his goal.