The Fast of Gedalya is equal in all aspects to the other public fast days. We have already explained these laws in the Halachot pertaining to the Seventeenth of Tammuz.

When the Fast of Gedalya is Postponed
Rabbeinu Yerocham writes that Gedalya ben Achikam was murdered on Rosh Hashanah but since it is forbidden to fast on Rosh Hashanah since it is a holiday, the fast was established on the day following Rosh Hashanah, i.e. the Third of Tishrei. Maran Ha’Bet Yosef (Chapter 549) quotes his words. Likewise, the Meiri writes that the Baraita in Masechet Sofrim states that Gedalya ben Achikam was murdered on the First of Tishrei and only because this day is a holiday did our Sages establish the fast on the day after. The Radak writes likewise.

We have a clear Halacha (Shulchan Aruch, Orach Chaim, 559) that when a public fast day falls out on Shabbat and is postponed until Sunday, if there is a Berit Milah (circumcision) on that day, the three hosts of the Berit Milah, i.e. the Mohel (circumciser), the father of the child, and the Sandak (the individual on whose lap the circumcision is performed) are exempt from fasting. For instance, if the fast of the Ninth of Av coincides with Shabbat, it is postponed until Sunday, in which case the three aforementioned hosts of the Berit Milah may eat on that day. There are several other situations where we are more lenient regarding a postponed public fast day than the actual date of the fast.

Thus, based on what Rabbeinu Yerocham writes that the Fast of Gedalya should have been observed on Rosh Hashanah and it is postponed only because Rosh Hashanah is a holiday, the Turei Zahav (authored by Hagaon Harav David HaLevi, head of the Levov rabbinical court and one of the greatest commentators on Maran Ha’Shulchan Aruch) writes that it seems that if there is a Berit Milah on the day of the Fast of Gedalya, the three aforementioned hosts of the Berit Milah need not fast as this is a postponed fast. Nevertheless, there is still an apparent distinction, for usually it is noticeable that the fast is postponed, for instance, if the Ninth of Av falls out on Shabbat, everyone knows that it should have been observed on Shabbat and only in honor of the Shabbat is it postponed. However, regarding the Fast of Gedalya where it is unnoticeable that the fast is postponed, for it is postponed in the same manner every year, it would seem that the three hosts should not exempt themselves from fasting. Similarly, Hagaon Harav Yehuda Ayash makes this distinction and writes that logically, one should not be lenient in this matter regarding every Fast of Gedalya; rather, one should only be lenient regarding a postponed fast which everyone knows is postponed. This is indeed the halachic ruling of Maran Harav Ovadia Yosef zt”l.

Thus, during a year when the Fast of Gedalya falls out on a regular weekday, it has the same law as any other public fast day and the three hosts of the Berit Milah may not eat on this day.

However, this year, when the fast is postponed in any case, according to all opinions one may act more leniently regarding this fast as opposed to other public fast days, as we have explained.