Within the scope of a project we work with external employees who require access to Microsoft Yammer, but do not need any other Office functionalities. How do we have to license this scenario?

Until the 1st of January 2017, Microsoft Yammer could have been acquired as a standalone subscription license (SL). After that, Yammer was integrated into Office 365, making an Office 365 license a requirement for its use.
However, there is an exception for external users: if an external users is invited to Yammer via external network functionality, this user does not need a Office 365 SL.

Sources:

Microsoft Online Services Terms, August 2017
Official Microsoft Office Support (https://support.office.com/en-us/article/Yammer-Enterprise-stand-alone-plan-to-retire-by-January-2017-eb421e95-134e-46f3-a37a-bedf489e3f0e), retrieved 2017-08-23