I want to improve battery life

If you mean battery longevity (aka Battery Health) there is nothing to do except charge it every night all night and never let it run flat.

If you mean the time it lasts per day...

There may be apps that are inherently incompatible with the iOS especially after an update

Start by removing any VPN or security apps. Apart from being totally unnecessary they are also a strong contender.

Many mainstream apps need an urgent update, for example NextDoor with iOS15 so go to App Store and scan through your apps for those that need updating.

While there, uninstall any apps you haven't used for some time. They are unnecessary update burden. 

Check the battery usage chart in battery settings for any obvious bad apps but not every background process is shown.

Any streaming apps or apps that can run with phone closed, or Clocks that hold the phone unlocked, always force close them afterwards, despite the accepted wisdom not to.

Check battery capacity is above 80% in Battery “health”. 

Only after all that do you need to do the simple stuff advised in

iPhone Battery and Performance - Apple Support

In extreme cases you can backup and restore to factory.