When you create a Membership Level you can also nominate one of more persons to be notified by the "Notify on New Membership" option at the bottom of Membership Level details.
It is up to the organisation to choose who should be notified, however if you have a membership secretary this would appear to be the logical person or your Treasurer could also be another person to be notified.
You may nominate more than one person if you wish. Likewise you are able change who is to be notified or remove someone simply by clicking on the cross beside their name.

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