SplinterGlossary: Battle Cooldown Period
A delegated card that was played during the last 24 hours by the actual user of the card (delegatee), cannot be played in battle by its owner until a 24-hour period has elapsed since the last time it was played.
The same rule applies if you buy or rent a card that is in a cooldown period from the card market or rental market. Cards that are in a cooldown period have a cooldown status which is distinctively marked in both the in-game interface and in PeakMonsters.
Note that if you combine cards that are in the battle cooldown period, the resulting card will not be in cooldown.
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