What access is required to move a task from one project are to another in CLM RTC. Any special access license, permissions?

you would need to be a member of both project areas with your role having a permission to save work item.

Especially from the Target Project Area :
Team Configuration > Your Role Selected > Permitted actions: > Work Items > Save Work Item(server) Create a Work item > Create a Work Item of a specific type > the work item type you are working with should be selected

hope this helps.

Just in addition:
To move a work item you need two permissions:
- You need the permission to save (create) the work item
- You need the permission to remove the work item from the old team area.

The second permission is called "Remove work item from team area" and is part of the "Save Work Item" section within the permissions.

Important Note:
The permission to remove the work item must be granted on the project area level itself.
Means if there is a team admin within a sub team who is not granted permissions on the project area level, he won't be able to move a work item.

Hope this helps,
Simon