most of the times Outlook not sending emails issue is due to weak or no internet connection so you check for yourself if that the case:
Make sure you're connected to the internet, then check to see whether you're working in Outlook online.
Examine the Outlook window's lower-right corner. You are not connected to your email server if it reads Disconnected, Working Offline, or Trying to connect.
On the ribbon, select the Send/Receive option.
In the Preferences category, choose Work Offline. In the lower-right corner of the window, you should now see Connected to Server.
In the Send & Receive group, click the Send/Receive All Folders option.
Check whether the message has been sent or is still in the outbox.