can i upgrade my mac book pro 2010

If you are getting the advisory pictured in this Apple tech document:

If your Mac says that a software update is required to connect to iPhone or iPad - Apple Support

that is the update that Phil0124 mentions. it only updates iTunes to work with newer iOS and iPadOS version. It DOES NOT affect the system software on your Mac. It is a short quick download that I've done several times for our older Macs without issue.

What macOS version is it currently running?

What happens when you connect the iPhone with a USB cable to the Mac exactly?

A 2010 MacBook Pro can update to macOS 10.13 High Sierra but no further.

It should still be able to connect to your iPhone with 10.13, but may require a firmware update for iTunes when you connect the iPhone.

SergioRWC wrote:

I have a mac book pro 2010 and it will no longer connect to my iPhone xr. do i need to buy a new mac book or can i update the mac book software?

The maximum High Sierra macOS 10.13.6 (17G14042) last update November 12, 2020

Just as Allan Jones says, that that quick download for iPhone connection is tiny. Download and install completes in under a minute. It is not something to be dreaded..