Taki Tamurai is a girl from Okinawa. She is a character from the 1989 cartoon series. Unlike the animated versions of Kesuke Miyagi and Daniel LaRusso, Taki was an original character created solely for the animated cartoon. Her story was that she resided in Okinawa and knew Mr. Miyagi, and lived in a community whose well-being was dependent on a mystical minature shrine. However, when robbers stole the shrine, her community suffered, and Daniel-san and Mr. Miyagi offered to help her recapture it.
It seemed most likely that Taki was based on Kumiko, as both were from Okinawa, and there was one scene where Taki attempted to walk a tightrope, telling herself "Ballet lessons do not fail me now", which suggests a connected as Kumiko wished to become a ballerina in the second film. However, unlike Kumiko, Daniel-san and Taki seem to have no romantic connection, simply working together with Mr. Miyagi as friends.
The 1989 cartoon series Karate Kid is generally considered non-canon as opposed to the films and 2017 Cobra Kai live-action series. This is also the only feature of Daniel LaRusso where he was not paired with a female love interest.