When does season two of the new 90210 start?

You're likely thinking of the reboot of *Beverly Hills, 90210*, which aired from 2008 to 2013. It was actually called "90210", not "The New 90210".

There was no season 2 of *90210* (2008-2013). The series ran for five seasons and ended in 2013.

There was a recent revival called "BH90210" which aired in 2019, but it only had one season.