Which character replaced Preston Burke as head of cardiothoracic surgery? The answer is Erica Hahn.
Erica Hahn replaced Preston Burke as head of cardiothoracic surgery at Seattle Grace Hospital. She takes over Burke's former position in season 4 after Burke leaves Seattle following his decision to end his relationship with Cristina Yang at their wedding.
Hahn is not a random successor: she is an accomplished cardiothoracic surgeon and Burke's longtime professional rival. Their rivalry began at Johns Hopkins School of Medicine, where Hahn graduated second behind Burke. She had already appeared as a surgeon from Seattle Presbyterian before transferring to Seattle Grace at Richard Webber's request.
Her arrival changes Cristina's professional life. Hahn is deliberately hard on Cristina, partly because she sees aspects of her younger self in her and partly because she distrusts Cristina's role in concealing Burke's hand tremor. Hahn later leaves the hospital during season 5 after becoming disillusioned with its response to the Denny Duquette situation.
Teddy Altman eventually becomes another important head of cardiothoracic surgery, but she does not replace Burke immediately.