If someone says “Tom broke another lamp,” does it imply that Tom already broke a lamp or that another lamp was previously broken by someone?
Depending on the context, it could mean either.
It looked like Tom finally had his clumsiness under control, but no. Tom broke another lamp.
Here it’s implied that Tom has broken lamps before (and perhaps other things too).
Dick and Harriet ran through the corridors, smashing light fixtures. Tom broke another lamp.
Here it’s clear that Tom is just one of several people breaking lights.
As Oldcat noted in a comment, another might even mean “different” instead of “additional”:
Tom didn’t break the lamp in the hall. Tom broke another lamp.