A Buddhist temple belonging to a Zen school (e.g., Rinzai, Sōtō, Ōbaku).
There are many famous Zen temples in Kyoto.
I did zazen at a Zen temple over the weekend.
In my youth, I trained at a Zen temple in Kyoto.
I stayed one night at a Zen temple deep in the mountains.
Every weekend, I sit in Zen meditation at a Zen temple.
寺 is the everyday, generic word for a Buddhist temple, whereas 禅寺 narrows the reference to a Zen-school temple.
counter for temples
Compound of 禅 (zen, 'Zen') and 寺 (tera, 'temple'), with rendaku voicing tera → dera.