It's been a long time since last time I worked on my website.
My hoster stopped now to support php 7.
So my question is : can I update directly from 1.4.15 to 1.6 ?
If not I don't find the old update 1.5 to download.

Thanks.

You find older versions here: https://www.zenphoto.org/news/older-versions-archive/ (There is a link from the download page)

So my question is : can I update directly from 1.4.15 to 1.6 ?

We cannot tell as we support and test updating from the last version only. Probably it will but problem might be the PHP version. 1.4.14 ist quite old and 1.6+ ist PHP 7-8 only. You have to try as noted here: https://www.zenphoto.org/news/installation-and-upgrading/