We have collected quite a lot of tabs over the years, and our users probably have some they use more than others:
Is it possible to allow the users to rearrange them with drag&drop?
I think it wont work easily with TabSheet, because you would need to extend the component client side, but if you build a server side composition using Tab, Tabs and some layouts you could use generic Vaadin Drag and Drop API to make it happen.
Probably easier to just roll your own tabs in that case.
You could also use ( instead of native drag and drop) sortable layout with a combination of tabs.
It will give you smooth transition for the drag and drop: sortable-layout - Vaadin Add-on Directory
That looked really nice. Especially the Trello-like example.
I worry that our users then would like to reorganize everything… 
For now this was a “nice to have” request from our users, so not sure yet how much effort we want to put in
For now I’ve suggested the following design to my PO:
TabSheet.suffix: cogwheel → Popover → Grid with drag&drop and Show/Hide checkbox + a restore button below