The Hebrew month that immediately precedes Tishrei is Elul.
Elul is the twelfth month of the civil Hebrew calendar and the sixth month when the months are counted from Nisan, the spring month associated with Passover. It normally has 29 days and falls roughly during August and September in the Gregorian calendar, though the exact dates shift because the Hebrew calendar is lunisolar.
Elul is especially associated with spiritual preparation for Rosh Hashanah and Yom Kippur. In many Jewish communities, people use the month for self-examination, repentance, charitable acts, and extra prayer. Ashkenazi communities commonly begin saying penitential prayers called selichot shortly before Rosh Hashanah, while Sephardic traditions generally begin earlier in Elul.
The shofar is traditionally sounded on weekday mornings throughout Elul, except on Shabbat, as a symbolic wake-up call before the High Holy Days. The month’s name came into Hebrew through the Babylonian exile and is related to the Akkadian name Ulūlu, associated with the harvest season. Elul is therefore both a calendar transition month and a major period of religious preparation.