After taking down your partner with Osoto Gari, if their arm is straight (and you still have your balance) while maintaining control of their arm, quickly lie down on your back, throw your leg over, and go for the armbar. If not, you can transition to side control or Kesa Gatame.

Kesa Gatame is a position where you control their head with your near-side arm, pulling their head off the mat (don’t let their head touch the ground). Your far-side arm grips their bicep, pulling their arm up while controlling it with an overhook—their arm is under your armpit (underhook). Your hip is switched, pointing forward, applying pressure on their upper body.

From Kesa Gatame, you can transition to either the armbar or Americana. To execute the armbar submission, bring their near-side arm—the arm closest to you, preferably in your armpit—prop it onto your bottom leg, trap the forearm with your top leg, and bridge up. To perform the Americana, bring their near-side arm onto your bottom leg, guide their forearm under your bottom leg’s calf, then do a technical stand-up, bringing your bottom leg back in a similar motion to performing the Americana with your hands.

You can check out this video demonstration of how to apply these submissions:

There’s also this stepover arm lock variation that I’d love to try:

Why choose Kesa Gatame over side control? Kesa Gatame offers better upper body control, while side control provides more room for mobility and transitions.

How to escape from Kesa Gatame: From the bottom position in Kesa Gatame, avoid going for the underhook. Instead, frame on their face and chin with both hands. Once there’s enough space, bring your leg up above their face and push down on their temple, which should be sufficient to escape.