"A Promise Kept" is a song written and composed by James Horner for the film Titanic. It is about Rose's promise to Jack before he dies (that she will live a long life, even if he does not survive the Titanic's shipwreck, and do everything she has wanted to do with her life). It was also featured on the film's soundtrack.
The film version of the song features the first part of the OST version yet the second half is significantly different, featuring synth flutes, atmospheric effects, synth voices, and a more mournful performance of Sissel scoring Jack's death (which is also heard in the main titles). The second half used in the film is called "A Promise Kept - 2nd Part Revised" and can be found on the 20th anniversary soundtrack.