I'll let the backstory explain:
On the outbreak of the Dominion War, Starfleet's Corps of Engineers (at the time headed by time displaced Montgomery Scott) was tasked to evaluate certain types to be brought out from mothballs to fill up the fleet's ranks. Chief among them were several Constitution type hulls of various configurations stored in various reserves. Evaluations by the SCE were promising and shortlisted several to be refitted with current weapons and technology. The first selected would be the USS Wyvern (NCC-2848), surprisingly well preserved in Starbase 34's holding area.
The subsequent modifications were primarily of a fighting nature, ironic considering the scientific configuration she once held. Scott's "off the shelf" refitting techniques proved useful, swapping new computers and weaponry to a typical 2370's loadout. The external appearance generally stayed within the Constitution II configuration to keep costs at a minimum. Forming a "neo-classic" profile that would basically be a light cruiser capable of general fleet defense missions. The Wyvern would be re-added back to Starfleet service with the provisional registry of NCC-78702, as a personal touch by Scott. This would give the illusion of a new-build vessel, a helpful ruse in wartime.
Nicknamed "Wyvern Refit/Subclass" by her engineers, several more Constitution II hulls would be upgraded to the same standard. Creating two dozen or so of these revived neo-classics. Performing decently well in combat and filling out gaps in the Federation's core worlds. With several Wyverns earning their keep in notable engagements, it proved that the old Connies still had some fight left in them. However, the Wyvern itself was still generally limited to its purpose and Scott himself has noted that there is room for improvement. He hopes that the Wyvern is simply a beginning of a journey to truly revive the Constitution for the modern era. The next chapter is yet to be written.