In a comment Moshe suggests that the book could be Recall Not Earth by C. C. MacApp. I have the book (though I don't recall ever having read it) and I can confirm this is the book described in the question.
The summary from Goodreads is:
All life on Earth had been destroyed in a quick and easy kill by the great and ruthless intergalactic Vulmot Empire. Only an elite group of spacemen survived the holocaust. The last earthlings, they were scattered wanderers through the galaxies, hiring out their fighting skills to whatever power needed them, yearly growing more bitter, dissolute, desparing.
By now the pitiful remnants of the Space Corps lacked even the will to fight - until a tantalizing promise from an enslaved race made them assemble one last time, for a mission only men with nothing to lose would attempt, for a final battle only desperate courage could win...
which matches the basic scenario described in the question, and the derelict starship was indeed built by a vanished race called the Klee. The location of the ship is revealed to the surviving Earthmen by a member of a race called the Chelki as part of a bargain with them:
The Omniarch returned the photograph to the envelope he'd taken them from, put the envelope in his folder, and laid the folder on the small table. "You have perhaps seen a few Klee artifacts, and heard various legends."
John shrugged. "Who hasn't? Bits of statuary, cast from metals no one can duplicate and that have lasted twenty or thirty thousand years without corroding. Smashed instruments that baffle the best of scientists. Kitchen implements, jewelry…"
"I," the Omniarch said, "know where I can get you a Klee ship, intact, powered, and operative. Not primarily a warship, though she has bays for weapons to be mounted. A very large ship. And I will help you solve the controls and instruments. I have made a considerable study of Klee technology and have made a few inroads."
The ship is taken by the Earthmen and (re)named Bertha.
The aliens that destroyed the Earth are called the Vulmoti. At the end of the book there is a confrontation with the Vulmoti forces during which:
The null space drive on the Bertha malfunctions and jumps ten thousand years into the future. The Earthmen find that during this time the Vulmoti empire collapsed and is now forgotten, and that the Earth is now inhabitable again.