When managing emails in Outlook, the way your mailbox interacts with the server depends on whether you're using IMAP or POP3. With POP3, emails are downloaded to your device and often removed from the server, freeing up space. IMAP, on the other hand, synchronizes emails across devices while keeping them stored on the server, which may eventually lead to a larger or full mailbox.

If you prefer to keep all emails, the best long-term solution is to request that your administrator increase your email storage space. This allows all emails to be stored on the server, where they can be accessed from any device connected to your account.
Additionally, storing emails on the server reduces the risk of losing important communications due to hardware failure, theft, or damage to your local device.

However, if upgrading storage is not an immediate option, here are some steps to free up space and keep your mailbox organized:

In Outlook, you can archive and store old emails locally on your device by moving them to a separate Outlook Data File (.pst). This file can be accessed in Outlook whenever needed.
To do so, please refer to this guide: Archive emails manually in Outlook