As requested, the story so far...
Kirk has been possessed by an alien known as Arashnievel who uses Kirk's authority to take the Enterprise to Omicron Centauri II so that he can take control of the "Great Machine" that resides there and so give himself limitless power.
Kirk/Arashnievel has a device which looks an awful lot like the servo used by Gary Seven in the TOS episode "Assignment: Earth" (currently McCoy has this device).
Arashnievel has been pursued by his daughter, Asharina, who is attempting to return him to The Origin
(no-one has explained exactly what that is, yet) for punishment.
Asharina has a shape-shifting starship which she controls via a mental link.
Early on both Kirk/Arashnievel and Asharina were subdued. Spock attempted a mind-meld to discover what was wrong with Kirk. But the mind-meld went awry and Arashnievel took possession of Spock's body as well as Kirk's (although Kirk's body remains unconscious).
While Arashnievel was mentally probing for the machine on the planet the "combined"
consciousnesses of Kirk and Spock manage to "piggyback" themselves onto his thought-waves only to find themselves on the planet where the "Great Machine" has manufactured them both new bodies.
Spock manages to use the "Great Machine" to transfer himself (in his simulated body) back to the Enterprise where he confronts Arashnievel (still controlling Spock's original body) and who is about to kill Asharina.
Asharina uses the distraction to psychically assault Arashnievel and also to project herself down to the planet where she meets Kirk.
...I think that's all the main points covered. Phew!!