Hello @Gary ,
Welcome to the community, and the ability to archive a project is not yet avaliable in Jira Cloud, but the feature is coming soon.
Check out the following community post from another user asking the same question but one of our Jira Software Project managers gave a full writeup on his answer discussing the features roll out plan of archiving projects in Jira Cloud:
And the feature is being tracked here:
As covered on the Feature the currently avaliable workaround option is to hide a project that no longer needs to be visible, by clearing out the project permissions. A breakdown of the workaround can be seen in the KB article "Creating, editing, deleting, and hiding projects" under the section: