The Spell says it last up to an hour with Concentration.

"You choose a creature you can see within range and mystically mark it as your quarry. Until the spell ends, you deal an extra 1d6 damage to the target whenever you hit it with a weapon attack, and you have advantage on any Wisdom (Perception) or Wisdom (Survival) check you make to find it. If the target drops to 0 hit points before this spell ends, you can use a bonus action on a subsequent turn of yours to mark a new creature."

The spell is cast during the first encounter. All enemy's are killed. I continue to concentrate on the spell.

A second encounter happens before the 1 hour duration expires. Say 20 minutes later after we stop to eat lunch.

Can I use a bonus action to mark a creature or do I have to recast the spell?

Is there a way to get an official ruling on this?

Thanks

Here's a tweet from the game's lead rules designer about Hex, which has the same wording as Hunter's Mark when it comes to moving it to a new target:

After the target of hex drops to 0 hit points, you can curse a new creature on a subsequent turn—doesn't have to be the very next turn.

Thank you InquisitiveCoder.