Will Keynote work on MacBook Pro running macOS Monterey 12.7.6?

The current Keynote (15.3.1) in the Mac App Store requires macOS 15.6 or later for installation, so in that regard, the answer is no for installation on Monterey.

If you have ever installed Keynote previously from the Mac App Store since Fall 2013, then you can get the last compatible version available for macOS Monterey. If you didn't, and it came pre-installed by Apple or a third-party reseller, then you are out of luck, short of signing into iCloud dot com and using Keynote there.

If you previously installed Keynote, then follow these steps on macOS Monterey:

1. Launch the Mac App Store
   1. Sign-in with your original Apple ID that you used to previously install Keynote
   2. Press cmd+0 (zero) to open the Purchased panel
   3. If Keynote appears on that panel, it will have some indicator that it can be downloaded. Click that.
      1. You will receive one or more dialogs, on which you do not click Cancel. The last dialog will ask if you want to install the last compatible version (13.1) of Keynote to macOS Monterey. You know that answer.
2. Quit the Mac App Store