Clarice Starling saves Catherine Martin, kills Buffalo Bill, and graduates from the FBI Academy with flying colors. Yay!
But the ending to The Silence of the Lambs isn't all one big party, even if there is an amazing looking cake with the FBI logo frosted on top of it. There's an unintentional trade-off for capturing and killing Buffalo Bill: Hannibal Lecter escapes. Clarice and the FBI have basically freed one dangerous psychopath in order to catch another.
Lecter is fascinated with Clarice, and he calls her with congratulations. He also promises never to go after her (i.e. sneak up behind her and eat her), and he asks her to do the same. "You know I can't make that promise," Clarice, ever the honest professional, says to the not-so-good doctor.
However, she doesn't know where he is. Lecter quickly gets off the phone, ending with a deliciously devious pun: "I do wish we could chat longer, but I'm having an old friend for dinner. Good bye." Turns out the sadistic hospital director, Dr. Chilton, is nearby. Lecter isn't planning on serving him a roast, of course. Lecter is planning on serving him as roast, and he stalks Chilton through the crowd as the credits roll. The anti-hero Hannibal Lecter lives to eat again another day, and he does in the sequel, Hannibal.
And let's be honest: there's something of a visceral thrill in knowing that Lecter is going to eat Dr. Chilton. Chilton's a creep and the general audience consensus is that he gets what's coming to him.