No, there is not one that contains every living organism.

“The world’s largest seed bank is managed by the Agriculture Research Service of the United States Department of Agriculture. It holds more than 460,000 seed samples and has the capacity to store up to 1 million.” SciDevNet

Here is an article on some of the largest.

Just cataloging all the insect species is no small task, let alone all the different types of microorganism

Famed Harvard biologist Edward O. Wilson advocated walking around rain forests with a vial of liquid nitrogen, dropping in all manner of tiny organisms in a last-ditch effort to catalog surviving species, as habitats continue to shrink due to human activity. I’m not sure if there’s actually any funded effort to do this.

It’s estimated that a large fraction of all existing species are still unknown to science, including millions of insect species alone. Liquid nitrogen would instantly kill a specimen, leaving its body intact and its DNA viable. (Sorry no references – I just remember watching an interview of Wilson.)

Every organism? Surely not. Absolutely not. Did you mean “every species”? That’s somewhat less daunting, but still a massive undertaking.

yeah there’s just absolutely no way in hell. and if it does exist, it’s surely quite the secret and well guarded.

@CWOTUS Yes, just one or a few of every species. (Ants & termites comprise something like one third of animal biomass, according to Wilson – don’t want all of them). Meant just for small invertebrates and such, I think. Presumably an expert with a microscope (or dna sequencer) could later classify the species of each specimen. Here’s one article where he explains the idea, then explains why it wouldn’t work to resurrect a lost ecosystem.

There is some momentum amongst the scientific community to cache DNA samples of endangered species, but movement is pretty slow as the moral and ethicall issues of cloning are kind of gumming up the works and slowing development. It makes sense to me though.