Is there a way to get a later version of Xcode on my MacBook?

What macbook? What macOS? Which later version Xcode are you after, exactly?

If you mean can you install current version 10.2.1 on an unsupported/older macOS of cryptic vintage, well, that would lead to a franken-install...can't help w/that.

If you mean are versions older than the current Xcode 10.2.1 still available, yes.

See the Xcode wiki for which version your macOS supports, then use this link - search there for the required version, download and manually install.

I had a situation recently where the Mac App Store would display an Open button on the Xcode page instead of the Install button, even though the version of Xcode I had on my Macbook was several versions behind the latest version. I had to delete Xcode from my Macbook (scary) before the Mac App Store would display the Install button for Xcode.