How can I update an older MacBook Pro?

For Macs, Apple uses the term "Upgrades" for major releases and "Updates" for minor ones.

An early 2015 MacBook Pro can be upgraded to the latest version of Monterey macOS 12 but no later. 

See instructions in: How to download and install macOS - Apple Support  

Be aware that if you upgrade to Catalina 10.15 or later you will also need to update any non-Apple 32-bit apps. See: https://www.stclairsoft.com/Go64/

or

 https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

Sorry, no. There isn't any hardware upgrade that would allow it to upgrade beyond Monterey,

Also see the following from Identify your MacBook Pro model - Apple Support

MacBook Pro (Retina, 13-inch, Early 2015)

Model Identifier: MacBookPro12,1

Part Numbers: MF839xx/A, MF840xx/A, MF841xx/A, MF843xx/A

Newest compatible operating system: macOS Monterey

What type of Mac (MacBook Air, iMac, etc), what model year is it, and what version of OS is it currently running? All 3 of those things are shown at Apple menu > About this Mac.