While it was not anime, they did make a Star Trek: TOS animated series in
the Unites States.  It only lasted 22 episodes however, they can be found
for sale at video stores like Suncoast.  I don't know if you can rent them
or not.

Warr

>From the volume of fan-fictions all of you write, this has probably been
done.  However, if not, I am interested in writing a fan-fiction that
takes the premise of:

What if Star Trek had been an anime?

The idea came as an idle thought and I thought I'd get some ideas off of
it.  If it has been written, tell me.  If this is inappropriate, tell me.
If the ghost of Gene Roddenberry is directly behind me with a Warp-drive
mallet, well, he'll probably tell me.  But barring that, or direct
intervention from Q, I'd like some response in any form.

Temee no tamashii, ore no!
(Your soul is mine!)
P.S.  The working title is: Sei ni ryokou de, hangyaku!
                           Star Trek:  Rebellion!

[snip]

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"When the father of John Doe, Jr. dies, John Doe, Jr. becomes simply John
Doe. That's the rule. As for John Doe III, he becomes John Doe II, when
either of the two men for whom he was named dies, then becomes simply John
Doe when both are gone. That, too, is the rule." So writes a client who has
made a lengthy study of the matter.