If you'll accept the Vonda McIntyre novelization as a source, it goes into some detail about this.
Apparently they have frozen humpback tissue on hand that they could clone. However, 1) it won't help with the immediate problem, because a cloned whale won't know any of the songs the probe is looking for, and 2) humpbacks are big-brained enough that they have to learn a lot of stuff from their parents or they won't survive, which is why nobody tried to reintroduce them before.
"If the probe wants a humpback, we'll give it a humpback," McCoy said.
"We've reintroduced other extinct species by cloning frozen tissue
samples-"
"The same difficulty remains, Dr. McCoy," Spock said. "The reason great whales have not been reintroduced to earth's seas is that
no great whales still exist to teach them survival, much less
communication. You could clone a whale, of course-but you would create
a lonely creature with no language and no memory of its own culture.
Imagine a human child, raised in complete isolation. Imagine. . . my
own existence, had you refused to undergo fal-tar-pan. No. A cloned
whale, crying its despair, could bring only further destruction.
Besides," he said, considering practicality, "I doubt earth could
survive for the years it would take to grow a cetacean to maturity."
At the end of the book, the combination of clones with genuine, culturally literate, 20th-century whales is supposed to suffice to repopulate the species, though neither would be enough on their own.
Samples of whale cells, preserved in the twentieth century, would add
to the species' genetic diversity through cloning. Legends and myths
to the contrary, two individuals-even three, when Gracie's calf was
born-were not sufficient to reestablish any species. The whales would
never again be hunted, and their freedom would never again be
curtailed.
