In beta canon it’s explained that, eventually, the humpback whale population of the 23rd Century is restored with the help of George and Gracie’s offspring together with cloned humpbacks from DNA stores, which establishes enough numbers for a breeding population.
(And to answer the inevitable follow-up question of "if they had whale DNA why did they have to go back in time?":
Cloning whales wouldn’t have helped because quite apart from not being able to grow clones in time, those whales would have no knowledge of whale songs - as Spock noted, they couldn’t just reproduce the sounds; they needed the meaning as well.
KIRK: Spock, could the humpback's answer to this call be simulated?
SPOCK: The sounds, but not the language. We would be responding in gibberish.
So the fact they didn’t clone whales doesn’t necessarily mean they didn’t have the genetic material. It just wasn’t a viable solution. One assumes George and Gracie would teach the newly cloned humpbacks about whalesong.)