I can’t add a Planner tab to a Private channel
Privately channels are a new feature to Teams sites.
Apps must be installed first to the Team site before being “Activated” in a private channel. If a team owner has restricted app installation to owners only, a private channel owner may need to request installation prior to adding an app tab.
Unfortunately, there are certain Apps (for instance Planner) which have a pretty tight connection to an Office 365 Group. Because the private channel has a site collection which is NOT group connected, those Apps are NOT available. It is anticipated that Microsoft will provide a solution, but there is no timeline on availability.
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