It has been stated in a number offical trek publications that the Enterprise-A was the recently decommisioned Yorktown.
We've also seen in an official publication that the Enterprise-A
was previously the transwarp testbed vessel U.S.S. Ti-Ho
(Mister Scott's Guide to the Enterprise
The origins of the Enterprise-A
are up to personal interpretation as we're unlikely to ever see it's story in a canon setting.