Is it possible to update a jailbroken iOS 7 to a version Apple has stopped signing?
Nope. It's impossible to upgrade iOS firmware without connecting to the Apple servers.

Currently, there is a jailbreak for iOS 8.1 using Pangu which is being signed at the moment. iOS 8.1.1 update which is due in a few weeks will patch the jailbreak. It could be the right moment to upgrade your iOS version and re-jailbreak it.  @saurik confirmed that the current iOS 8 jailbreak is stable.