How do link SharePoint Lists beetwen different sites in SharePoint Online?
How do that? Is there solution for that?
The only way I know of to do this is using a third party tool. Content Query Web Parts do not work across site collections. The tool that comes to mind first is the Lightning Conductor Web Part from Lightning Tools. It can roll up data across site collections and farms and display that data in a lot of customizable ways. There are probably other web parts out there that work similarly. The only other option I could think of without doing a third party tool is creating a page that has a minimal masterpage and put a view of the list on there as a web part, then using the page viewer web part to show that data in the second site. However, permissions must be set so that users will see what they are supposed to see in that page viewer, and not receive "access denied."
As a general rule you cannot link lists between sites using standard SharePoint OOTB controls, however, it is possible to do something very similar using site columns.
If you create a site column in your root site, it will be available on all of its child sites i.e. the site column Contacts in the root of the site could be used by the Contracts list on any other site beneath the parent.
There's a good overview of SP Columns here: http://msdn.microsoft.com/en-us/library/ms450825.aspx