You can either to use the same SharePoint site for TFS that you have right now or you'll need to upgrade your SharePoint instance first.
- TFS 2010 supported Office SharePoint Server 2007 (Standard,
Enterprise) and Windows SharePoint Services 3.0.
- TFS 2015 supports SharePoint 2010 and 2013 (Foundation, Standard,
Enterprise).
After upgrading your SharePoint instance, you'll need to install TFS 2015 on it and then configure SharePoint Extensions.
Here's a guide on how to migrate TFS databases including SharePoint databases in detailed steps:
Migrating Team Foundation Server Databases
This is also a related situation for your reference:
Migration Update from Team Foundation Server (TFS) 2013 to TFS 2015 (With Reporting and SharePoint)
Update
Things That Don't Work Anymore After I Migrated to SharePoint 2013
The change from SharePoint 2010 to SharePoint 2013 is even more
radical then it was from SharePoint 2007 to SharePoint 2010. This time
we’re switching to HTML5 - which was built to work easily on all
browsers and even other devices. In today's world, it was inevitable.
There is also a big change in the way SharePoint shows us its content;
Web Parts no longer use tables, for the most part, and the use of XSLT
has been replaced by Display Templates. This means almost all your
branded Web Parts and Content Query styles will no longer work. ....
Source Link: What might not work so well anymore after the
migration
And according to TFS 2013 Upgrade - SharePoint 2010 to SharePoint 2013 Failure. SharePoint 2013 has two modes (hives), 2010 (v14) and 2013 (v15). Apparently,a new 2013 installation mostly only installs v15 features. You can also give a try with this.
I don’t think all your old look and feel will be functional in 2013, given the huge changes in the UI. But since that site’s content and TFS function is fully browsable and usable as it is now with old look, at least you can still remain in 2010 mode.