Restoring emails deleted from trash

If you deleted them from trash they are gone unless you kept a backup of your emails. You could also log into your email accounts using the provider's web page and check if the provider maintains an archive of old deleted emails.

Hi: I have a Macbook Air running Catalina 10.15.7.

This morning as I tried to set up a new display I moved my files from the desktop into the bin and deleted them. I have tried to find the "trash" file to recover them but its nowhere to be found ? I have restarted my machine but am a bit lost ...

can anyone help please?

If you removed the files from the bin, they are gone and not recoverable. You can recover them from your backup, if you created a backup.