The tabs displayed on a project are governed by the page layout the project is linked to.
1. Add the Page Layout field to the project list view and note the Page Layout the project is linked to.
Let say it is the 'Project Default Layout'
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Note: You can add this view to the project properties but you can also go to 'Home' -> 'Project's -> 'Options' (cog wheel icon on right side of the screen) >' Configure' > 'List Column Section' tab > move over 'Page Layout' from 'Available Columns' to 'Selected Columns' > click 'Save And Return' and you will see the 'Page Layout' column at the list view
2. Go to 'Administration' > 'Portlet Pages' > 'Project Default Layout' > 'Tabs' tab
Check if 'Processes' tab is ticked.
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If the Processes tab is active on the associated Page Layout, but the project does not display it, it might be that the layout itself for that project has got corrupted.
3. Change the Page Layout, from the 'Project Default Layout' to any other layout available.
Save the changes and reset it back to the 'Project Default Layout' or the Page Layout that was originally set
<Please see attached file for image>