Tate-shiho-gatame (縦四方固), the vertical four-quarter hold.

Osaekomi-waza (hold-downs).
Required for: 6th Mon (yellow belt, British Judo Association); 8th Mon (orange belt, British Judo Association); 5th Kyu (yellow belt, JudoScotland); 4th Kyu (orange belt, JudoScotland); 3rd Dan (black belt, British Judo Association); 4th Dan (black belt, British Judo Association); 5th Dan (black belt, British Judo Association).
Also known as: full mount (bjj).

About
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Tori sits astride uke, chest down, controlling an arm and the head: the mount position of judo.

Step by step (standard right-handed form)
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1. Your partner lies on their back; step across and sit astride their body, your seat on their belly, knees on the mat either side.
2. Hook your feet under their thighs, or cross your ankles beneath their legs, so their bridging cannot simply tip you off.
3. Wrap their right arm and their head together with your right arm, gripping cloth or your own leg, and bring your chest down onto theirs.
4. Keep your head low beside theirs on the wrapped side, your left hand posted wide on the mat for balance.
5. When they bridge, float with the movement, hips loose, and let your hooks and chest bring you back down; riding the bridge, not fighting it, is what keeps the hold.

Key points
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1. Sit astride with your hooks in or feet locked under uke's legs
2. Control uke's arm and head, chest heavy
3. Ride uke's bridge with loose hips rather than fighting it

Receiving it
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They sit astride your body, chest coming down onto yours, your arm and head often wrapped together, their feet hooked under your legs. Bridging throws them forward but the hooks bring them back, so combine it: bridge, turn, and hunt for an elbow or a hooked foot to free. The position feels dominant and heavy; keep your breathing low, protect your neck by keeping your chin down, and tap clearly if you need to stop.

VI judo notes
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Astride them, your seat and chest report everything, so hold by riding rather than by clamping. Wrap their arm and head together on one side and keep your head down beside theirs on that side, since that is where you will feel a turn start. Hook your feet under their thighs so a bridge lifts you instead of tipping you, then float and settle back down.

Reference pages elsewhere
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Tate-shiho-gatame on the IJF technique reference (International Judo Federation): https://judo.ijf.org/techniques/Tate-shiho-gatame

From Waza Book: https://wazabook.com/techniques/tate-shiho-gatame/