Do Zen Buddhist believe in Reincarnation?

Yes & No

Taisen Deshimaru, Zen Master & the New Orleans Zen Temple said that Belief in Reincarnation is unimportant.

Only Zazen is important.

I don't think that Zen Buddhist spent much time investigating or thinking about Reincarnation.

Most anyone can attend the New Orleans Zen Temple for a limited time or retreat.

there website is www.nozen.org . . .

Tibetan Buddhist are conditioned from birth that we have had a previous life and will reincarnate.

Belief in Reincarnation has good evidence from the University of Virginia & the 40 years work of Dr. Ian Steveson.