LinkedIn Sales Navigator does not include a way to export your sales leads directly. Instead, you would need to search for leads, and click through each one to see then copy their contact information. Or, if you add the leads as contacts first and they accept you, LinkedIn lets you export your personal contacts from your My Network page—though would need to re-export whenever you need new contacts, and if you are looking for a large number of leads, you could quickly hit LinkedIn's 30,000 contact limit.
The only official way to export leads out of LinkedIn Sales Navigator is with the built-in Salesforce sync. If you have a Salesforce account, you could set LinkedIn to sync your leads to Salesforce. That'll give you all of their contact info—including email address—in Salesforce, where you can then export a spreadsheet of your Salesforce leads or use other Salesforce integrations to sync contacts from Salesforce to your email newsletter, marketing apps, and more.
Or, you could use 3rd party browser extensions to scrape extract emails from LinkedIn Sales Navigator—including Wiza and Skrapp.
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