Due to code base changes you can’t do a upgrade in one step, you’ll need to do this step by step.
That being said, have a snapshot or backup. At some point you’ll also have to upgrade your OS due to Debian 8 being end of life.
The following should work:
Please ensure that your repository (mainly URL and path) is fitting our current requirements
If the current installed file differs, remove it and install the new version as described below
Everytime you updated the repository file an friendly apt update; apt install zammad should do.
Please do note that After 3.4 Installation you have to change your distribution. Upgrading would be the easiest pick without backup and restore - if suitable. You have to adjust Zammad repo files as well.
Keep in mind that elasticsearch has specific upgrade path - a destructive but faster way is to remove the indice directory of elasticsearch - that is if Zammads index data is the only thing living there.