Although we do not bless the new month on this Shabbat, it is the Chabad custom to observe all of the customs of a regular Shabbat Mevorchim, specifically to recite the entire book of Tehillim and participate in a Chassidic Farbrengen. We observe these customs because there is a tradition from the Ba’al Shem Tov that G-d Himself blesses the month of Tishrei rather than the Jewish people who bless the other months.
- Av HaRachamim is recited before Musaf.
- Tzidkat’cha is recited at Shabbat Mincha.
- See here for several connections between the week’s Torah portion and Rosh Hashanah.