A supplementary ticket allows you to use bus or train services outside the area for which your season ticket is valid. It is valid for 1 journey in 1 direction and you need to buy it before you start your journey.

To see which supplementary ticket you need, count the fare rings you need to travel through which lie outside the fare zones on your season ticket.

For example: you want to travel from Hauptbahnhof to Bargteheide. If you have an all-year or monthly season ticket for the 2 zones 000 and 105, you will need a supplementary ticket for 3 fare rings (A, B, C), since you need to travel through fare zones which lie in 3 rings outside those on your season ticket.
If you have a monthly season ticket for the 3 zones 000, 105 and 205, you only need a supplementary ticket for 2 fare rings (B, C), since all the zones you need to travel through in A are already covered by your season ticket.

 Fare zone plan