If the first triggered ability of suspend (the one that removes time counters) is countered, no time counter is removed. The ability will trigger again at the beginning of the card's owner's next upkeep.
The Eleventh Doctor
Due to a recent rules change to suspend, you are no longer required to cast the suspended card as the second triggered ability of suspend resolves. Instead, as the second triggered ability resolves, you may cast the card. Timing permissions based on the card's type are ignored. If you don't cast the card, it remains exiled with no time counters on it, and it's no longer suspended.
You can exile a card in your hand using suspend any time you could cast that card. Consider its card type, any effects that modify when you could cast it (such as flash) and any other effects that stop you from casting it (such as from Meddling Mage's ability) to determine if and when you can do this. Whether you could actually complete all steps in casting the card is irrelevant. For example, you can exile a card with suspend that has no mana cost or that requires a target even if no legal targets are available at that time.
Magic: The Gathering · ™ & © Wizards of the Coast · Illus. Tyler Walpole
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