After installing Lightroom Classic v 15.4.1 and updating catalogue, I can no longer open LrC.

Unfortunately you haven't given us deteiled informations about your issue and any informations about your system. Therefore, all proposed solutions are a little bit of guesswork.

Do you get any error messages? If yes, please post the messages here.

Does the update of the catalog work without error?

First try a reset of the preferences of LrC:  How to reset Lightroom Classic preferences (adobe.com)

It's recommended to backup your preferences before you reset the preferences to the default settings: https://helpx.adobe.com/lightroom-classic/kb/preference-file-and-other-file-locations.html

If this doesn’t help create a new catalog and see if LrC starts.

Hold the Ctrl-Key while starting LrC. This opens a catalog selection dialog.

Click on “Create a New Catalog” to create a new one and see if this catalog works. If yes, you could then try to import your current catalog into the new one.

If this also doesn’t help, please provide a copy of your 'System Info'. This can be get from the Lightroom menu item Help > System Info. There's a copy button in the System Info dialog. Press this button and paste the info into your next forum post.