I recently hosted few websites at Linode without setting up mail server. And I don't like to set it up here.
Is it possible that I can use my old shared host to do this job of mail sending/receiving?

If you're currently using the other host for your email needs there no reason it couldn't continue to serve that role. You would just make sure that you have the proper DNS entries that point your email to the old host and point your websites to your Linode IP address. Based on your website software and your control panel of choice you may have to change how each is configured to use email.