Update my iPhone to iOS 15

Assuming you have a compatible device, see: Update your iPhone, iPad, or iPod touch - Apple Support

And: If your iPhone, iPad, or iPod touch won't update - Apple Support

If the above Apple articles do not help, please post back with relevant information. 

NOTE: Any update will be to the most recent, compatible version of iOS.

Are you now running iOS 15, or do you want to update to iOS 15? Either action depends on the MODEL of your iPhone.

If you want to update TO iOS 15, your phone model must be listed in this Apple Support document:

iOS 15 and iPadOS 15 are compatible with these devices - Apple Support

If you want to move FROM iOS15 to iOS 16, your phone model must be listed here:

iOS 16 and iPadOS 16 are compatible with these devices - Apple Support

Update your iPhone or iPad - Apple Support

Update iOS on iPhone - Apple Support

About iOS 15 Updates - Apple Support

[Link Edited by Moderator]