One of the things that makes Terry Pratchett's work such fun is that it is constantly evolving and changing. A number of fragmentary ideas don't entirely work, or get boring, but he uses them to keep growing and changing. DEATH is a marvellous example of that kind of growing evolution.
In Mort, DEATH'S first book, Pratchett makes him (only in some ways) the stereotypical death. The dark cloaked skeleton with the scythe who rides a pale horse and appears when someone dies. But even in Mort, there are some indications that Terry is going to use him in different ways. DEATH is very good at his job, but he has also become very intrigued with humanity. He is trying to learn "what makes them tick." Thus, he "adopts" Ysabell and keeps her at 16 years old until he decides she should marry, and then brings in her future husband, and while Mort is acting in DEATH's role, DEATH is learning more about humanity.
In DEATH'S next, and very significant, development, he is "fired" either by the Auditors, or at their instigation. In Reaper Man he really begins to understand humanity (it's fears, hopes, loves, loyalty) as Bill Door who is saved from the new Death by Miss Flitworth's unselfish gift of time and a kind of love, which he returns the only way he can--by giving her a "night to remember" and returning her at her death to her own true love.
In this book DEATH has mysteriously disappeared, which leads to the development of his granddaughter SUSAN who while partially human, also shares his powers. And while most of this book is about the education of Susan, significantly, DEATH, who acts like (as does almost everyone else in the book) a teenager--takes the hot rod "motorcycle" and the Dean's Leather's and rides off after his granddaughter and the others. While the motorcycle dies--and DEATH apparently crashes with it, he has the ability to re-incarnate himself, and the wisdom to deal with the problem of music that wasn't intended for Discworld. Thus, by breaking all the rules, he makes them work, and co-incidentally saves the band, who are no longer a band, and begins the relationship with Susan that will grow and develop through the rest of the books.
Soul Music is a transitional book, looking back and forward. It has some of the old style jokes (punning on names of bands, etc.) but it also deals in a small measure with the nature of time and how Time is used by and changed by humans.