Will there be a software update for a Macbook Pro (early 2011)?

Your model is obsolete. There won't be any updates. However, there are upgrades for the OS. Your model can be upgraded to How to upgrade to macOS High Sierra.

Before You Upgrade macOS

1. Fix any problems before upgrading.
2. Run First Aid in Disk Utility while booted from your Recovery HD.
3. Backup. Make a bootable clone using CarbonCopy Cloner or use TimeMachine.
4. Be sure your startup disk has 18-20GB of free space during the installation.
5. Upgrade third-party software for compatibility. See App Compatibility Table - RoaringApps. If you have mission critical software, then DO NOT upgrade until you know that software is compatible with the version of macOS you are about to install.
6. Disconnect all third-party peripherals.
7. Download the installer which will be in the Applications folder. Quit the installer after it opens, then make a copy of the installer and save it in the Downloads folder. The one in the Applications folder will be deleted after a successful installation.
8. The download is large, anywhere between 5 and 9GBs. It takes time to complete. Be patient.
9. Double-click on the installer in the Applications folder. Click on the start button to begin the installation.

To learn how to update macOS, please read Keep your Mac up to date.

Hi,

High Sierra 10.13.6 is the latest for your MacBook Pro.

https://support.apple.com/en-us/HT208969

That's correct.