Hello,
I will divide my answer into two parts:
It seems simple that at times of war, there is penultimate importance to the Prime Minister being at their full capacity in Israel. A soldier mobilized on Shabbat to assembly areas must travel on Shabbat, all the more so when dealing with the Prime Minister. Not only this, but even when he is in Israel and there is a vital need for his travel on Shabbat – he is obligated to do so. Victory in war is not only a battlefield concept, but an essential state policy. It does not matter who the Prime Minister is, and in the past I have written about this in the case of terrorists breaking out of prison and the Prime Minister traveling to the command center with the assumption that he must made immediate decisions that can only be made in the field, see the aforementioned essays – link 1, link 2.
However, the sanctity of Shabbat and its significance require us to do two things before ruling he should return on Shabbat. First is to evaluate if this can be prevented, such as by assessing if the trip is necessary or if there is an alternative, whether to bring the flight forward so he is not flying on Shabbat, shortening the duration of stay and returning before shabbat, etc. In other words: to do everything one truly can so that the matter does not occur, similar to infinite other halachic topics where we try to do two things at once: both preserve Shabbat as a whole and fulfill the obligation of pikuach nefesh and the halachot of governance.
Second is that one should truly dedicate all their time to work only if it is for the purpose of accomplishing the goals of the war and the victory of Am Yisrael, and not to benefit from the obligation to return on Shabbat.
In order to remove doubt, and I have already written this above, it does not matter who the Prime Minister is, and my response does not deal with a specific case, but the principles and proper conduct for any Prime Minister in the past and future.
All the best,
Rabbi Yuval Cherlow
Head of the Tzohar Ethics Center
For additional reading: