Does the problem extend across the entire clip as a constant factor? IOW, is the whole music track just 1.01x too fast or too slow (or some other number like that)? Or is the problem specific to certain sections of the clip - is the music in time up to MM:SS:FF but then it drifts off over the next bit?
If the problem is the former, click on the audio clip, then click on the Properties tab. Notice that you can adjust the speed of the audio clip:
