Kage-Tsuki is the lead hook punch of Karate. It’s way diffrent from the lead hoo that you might see in boxing, at least the traditional form is, for example it doesn’t involve shoulder rotation and has minimal foot movement, and that’s why many don’t use it in traditional Kumite.

Traditional execution:

• Get in Kiba Dachi
• Close your fists
• Bend an arm to 90° and bring it to your center while performing an hiki-te with the other arm
• Kiai! at maximum extention (optional)
• While retracting perform another move (e.g: another Kage-Tsuki)

Kumite execution:

• Get in Kumite no Kamae and bounce a little
• Bend an arm to 90°, rotate it until you go back in guard and twist your foot, hip and shoulder in the same direction of the arm
• Simultaneously protect your face with your other hand
• Kiai! if you are competing in point sparring
• Unless you are doing point sparring, don’t retract or the punch will lose its force and purpose

Where to use (✅ - Use; ❌ - Don’t use; 🟨 - Last resource):

• Sport Kumite: ❌
• Full-Contact Kumite: ✅
• Self-Defense: ✅

Video examples:

• 8. Kagi Zuki