It is possible to create new and previous school years through: 
1. Navigate to Core > Settings > School information
2. Select the Years & terms tab.
3. Under School Years, click Add.

If a school is unable to create previous school years, it is due to the Alumni role being set to inactive.
To active the Alumni role:
1. Navigate to Core > Security > Roles
2. Under Constituent, click the Alumni role
3. In Role Properties, mark the Active checkbox