It is customary in Chabad circles to say Tehillim at this time. In addition, as mentioned above, one should recite Tehillim at every opportunity during the 49 hours of Rosh Hashanah.
Chabad custom is to begin Kabbalat Shabbat from Mizmor LeDavid (Psalm 29). The words “Berina Uvetzohala” are recited at the end of Lecha Dodi rather than “Besimcha Uvetzohala” as is recited on other Yamim Tovim.
Nusach Ashkenaz begins with Mizmor Shir LeYom HaShabbat (Psalm 92).