You can enable archiving mailbox on Exchange 2013 the following steps :
- Open Exchange Admin Center and Click Recipients and select Recipient which you want to archive click Edit:
2. in the opening window click mailbox features and scroll down click Enable under “Archiving: Disabled”:
3. Click “browse” and select the Archive Database which you want and Click Ok
After that user need to close and re-open Outlook and then you see Archive Mailbox which will show in the left side as “Archive – Test”