Possible Clues:

• Charles and the Queen making a drink
• One who pursues - one drink after another
• Drink for Grand National runner?
• The horse gets a drink afterwards
• One who pursues
• The one that's after you may come after with a drink
• National competitor that's put out in the second round?
• Hunter, or other kind of horse
• Catch a server to grab a second drink
• Drink that follows a shot