If a folder is deleted from clearcase and then when I "update from repository" should the folder be deleted locally also ? Currently it is not deleted locally, I have updated my view and can see the folder has been removed from the view.
No, by default, a cleartool update preserve private content.
And your directory is now considered private, once removed from ClearCase from another view.
(which is your case here: you didn't delete it directly in your view from the ClearCase interface).
You could see your directory renamed as 'yourDirectory.unloaded', but sometimes it will remain unchanged, especially if some process has an handle on it.
See technote "About .unloaded snapshot view files" for more.
The help page "How files and directories in snapshot views are unloaded" mentions:
Directories are unloaded recursively.
To unload a directory element, the files in the directory are unloaded.
If any view-private objects, hijacked files, or checked-out files are in the directory, or if the directory is currently in use (for example, if your current working directory is in or below the directory).unloadedis appended to the name of the directory.
For example, if the directory src contains view-private files, the directory is renamed tosrc.unloaded.
In your case, you need to make sure that no process has any handle on the directory itself or the directory content, make your update (-overwrite has no bearing here, being only there to restore hijacked file), and then search and remove any *.unloaded elements (files or directories).