Here's a documentary about the original construction of the Galileo 7 shuttlecraft, just mentioning the start of its recent restoration.
Original Star Trek Galileo Spacecraft--Where Is It Today?
A gallery showing what it looks like now that restoration is complete:
Galileo restored photo gallery
A newspaper article:
Restored Star Trek shuttle getting closer to Houston
And the Facebook page of the restoration project:
Shuttlecraft Galileo Restoration