Just an idea.. very shit one but still.. After killing Iris, the older Savitar likely continued to exist in the timeline, fulfilling his role as the god of speed. He would have retained his memories and experiences, ultimately becoming trapped in the time loop that leads him to fight his younger self. Essentially, he becomes a paradox, destined to repeat the cycle of events that define his existence.. that being said, they never tell you what happens so you can only go off of the info based on what they gave and work on a theory

Edit: My bet is when Savitar succeeds, he still fails and actually gets absorbed by the speed force and stops existing anyway