What comes before and after Yom Kippur?

New Year = Rosh Hashana . This is the start of the days of atonement during which Jews assess the way they act and attempt to make amends. It lasts for two days. This is followed by 7 lesser days of atonement. The last of the 10 days of atonement in Yom Kippur. 5 days later is Sukkot. On this festival, Jews build huts (called Sukkot on sukkah in singular). It commemorates the travel across the desert and also the harvest time. In Israel it is celebrated for 7 days. Some people mistakenly think that it lasts 8 days, but in fact the eighth day is a separate festival known as Shemini Atzeret which literally means (confusingly!) the eighth day.

Rosh Hashana comes before. Sukkot comes after.