By default Microsoft Outlook is configured with OST or PST file size restrictions. If your data file will grow up to the critical value, you will be notified first and then Outlook will block the write operations. Then you have several possible ways to continue work with Outlook:

1. you may remove the old emails and compact the PST file to reduce its size and make more space available;

The maximum default PST and OST files size per Outlook version:

• Outlook 2016 - 50 GB
• Outlook 2013 - 50 GB
• Outlook 2010 - 50 GB
• Outlook 2007 - 20 GB
• Outlook 2003 - 20 GB

Earlier versions of Outlook do not support UNICODE personal folders (.pst) and offline folder (.ost) files and the limit is set to 2 GB.

2. you may increase the limit value defined by Microsoft by default by modifying the Windows System Registry values.
Read how to configure the size limit for both (.pst) and (.ost) files in Outlook in Microsoft support articles.

Note that outlook data file size may be also restricted by the file system type and other factors.