Most ISP's will not allow outgoing email to be relayed through their system then out from your hosting account.
This is done for security and Spam reasons.
You will need to use your ISP's email system to send your outgoing email.
You will be able to receive email through your new hosting account.
Setup instructions to do this are below.
Note: Sending email from your hosting account will be possible if you login using the webmail system.