I have just bought a new imac 24in and imported the Mail app from my Laptop (9 year old MacBook Pro). However it has not imported everything and the inbox content stops at almost 3 weeks ago. This is for Gmail. What is wrong?

You can't delete the Mail app itself, which wouldn't help anyway. You can however remove the affected email Account(s), and add them again.

Refer to If you can’t send or receive email on your Mac - Apple Support. It suggests using the email service provider's webmail interface, and confirm messages appear as expected in it. If they do not appear then look in its Trash or Junk or Spam folders or their equivalents. If you can't find them anywhere then there will be nothing to retrieve.

The final step in fixing Mail app's missing messages is to Remove your email account, then add it back.

First remove: Log out of or remove email accounts in Mail on Mac - Apple Support

Then add: Add email accounts in Mail on Mac - Apple Support

Be sure to heed the Important note in the first document.