יִפְקֹ֣ד יְהוָ֔ה אֱלֹהֵ֥י הָרוּחֹ֖ת לְכָל־בָּשָׂ֑ר אִ֖ישׁ עַל־הָעֵדָֽה׃
“Let the LORD, Source of the breath of all flesh, appoint someone over the community"
Moshe understands that his end is near and so he asks HaShem to appoint a new leader.
Why does he do this? Moshe must have known that if a leader was necessary, then HaShem would appoint one and if not, what is the point of asking?
When it comes to prayer for oneself, a similar question can be asked. But there is a difference. I have heard that the prayer for one's own needs, changes the person and hence HaShem can change the fate already arranged for him.
In this case, Moshe is not davenning for himself but for Klal Yisroel. Even if he is changed by this fine act, (the rest of) Klal Yisroel remains unchanged.