If you hold a battlefield and move a unit away (making it open), then move another unit to that same battlefield, does the 'when you conquer' ability trigger?

Ruling: No, you cannot trigger the conquering ability because conquering is a subset of scoring. If you can't score the battlefield (because you already hold it), you can't get conquer triggers.

Nuances:

• You can score the same battlefield twice in a game, but not while you already hold it
• The same principle applies to abilities as it does to scoring