If you also have webmail access to your mailbox, have you checked whether that shows new messages or if it matches what you're seeing locally? If webmail is the same then the issue is at server end, while if it does have new messages then obviously the client
is the issue.
If you know the issue is client side, or you don't have webmail access to check, if your mailbox is very large then it's possible that your local .ost copy of your mailbox has become corrupt. If that happens Outlook doesn't always handle it well and won't
download new messages. If that's the case you can reset the ost by renaming it, letting Outlook re-create it and re-download your email. To do that, go to File, Account Settings, Account Settings..., select the Data Files tab, select your mailbox and you should
see the filepath to your .ost file listed. Click Open File Location so you can view that file. Close Outlook, rename the .ost to something else (just in case, rather than delete it at this point) and then open Outlook again. It will automatically create a
new .ost file, and will then download your email again and if that was the issue it will receive the missing messages. Note, if you do this do NOT close Outlook until it shows "All folders are up to date" at the bottom, eg it has finished downloading
everything, as otherwise you risk corrupting the .ost file again.