Assuming you successfully applied scissor leg tip, and now your opponent is on his back, with your legs around him, like on the image:
What move will you recommend afterwards?
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I usually choose between the following options.
Taking back your top leg is the most obvious but most complex follow-up to kani-basami. It requires some flexibility and dexterity, and your opponent can make it difficult, especially if they can grab your pant leg or shoe. But if they don't, it's feasible to pull your top knee to the mat as you turn and face the opponent chest-to-chest. From there you play your normal top game.
After finishing the throw, it's possible (as long as your bottom leg can be freed) to come up to this odd top position directly. A foot-facing mount offers some submission and transition options. I find it primarily useful as a temporary pin to make sure they don't scramble away after the throw. My other main choice from this position is to not stop here at all, but immediately transition to a kneebar on their near leg after I've come up on top.
The simplest option leaves your legs mostly in place, and because it requires the least additional movement it is often the fastest choice. The idea is to keep your legs mostly where they are, possibly upgrading to the most over-named position in BJJ: the leg entanglement known variously as the saddle, honey hole, 411 (four-eleven), cross-ashi-garami, or inside-sankaku. Whatever you call it, it should be quite near from where you find yourself after executing a leg scissor throw. One solid option from the saddle (etc.) or even just the finished-kani-basami position itself is to immediately attack the legs with a heel hook or toe hold.
It doesn't always matter what happens after you finish throwing with kani basami. In judo, the match is hopefully over with an ippon. (If not, you can turtle up and defend until the ref stands you up.)
The scissors-kick or Kani Basami (judo) is often done in case one of the throws you tried failed. If you don't succeed, you'll end up falling to the ground in a potentially vulnerable position.
And a quick warning: Kani Basami has been banned in competition Judo. There is an elevated risk of knee injury to the one receiving the throw. You can google to read more about that.
Probably the quickest grappling maneuver to achieve from this position is a knee bar or a heel hook. Again, you can look them up on google to find videos showing the techniques.
My preferred follow-up to this technique is to sit up towards him while leaving my right leg on top of him. As I'm doing this, I slide my left leg out from under his legs. I then reach a kneeling position with my right knee on his stomach or chest. That allows me to put all my weight down on that right knee while I lift my left leg up and over his legs to come to rest at my left side. This is the knee-on-chest position from the side.
When you do this, you'll find it's a pretty fluid transition. Your knee is right there. All you're doing is keeping it there while rolling that knee from the side of the knee to the knee cap, and sitting up while you're doing this. You have to make sure not to lean forward when you do this, because you can easily be unbalanced and pulled forward.
I've got a number of things I can do from this position (knee-on-chest). One is to get in some quick punches to his face. I can also get to my feet real quickly in order to run or deal with other attackers. I can drop into a juji gatame (arm bar). I can get mount. If he rolls over to his side to try to get my knee off of him, I can get a rear naked choke. Or if he rolls over to his stomach, I can re-place my knee onto the hollow under his shoulder blades (painful) while extending his arm out for an elbow lock. Plenty of options.
Knee-on-chest prevents him from reaching my head with his punches. It's good for defense. But it's a transitional position, because it's not likely that you'll be able to stay in it. Your opponent feels a lot of pain from your knee pressing into him. He's going to panic and will do everything he can to get you off of him. When that happens, you have to move to a better position.
So think of it as a mobile position. You need to be able to quickly move from it to something else. This is an important position for consideration for practical street self-defense, because your opponent may have a knife. You'll be in a better position to deal with a knife here than in many other ones. That's because you can see what's going on, first of all. Secondly, you can control his arms. And thirdly, you can very quickly disengage and run away.
If you don't think you can transition to knee-on-chest from kani basami, you might be able to transition quickly to side control. You sit up as quickly as possible and put your chest on top of his chest. While you're doing this, you can throw your legs out behind you. Consider judo's yoko-shiho-gatame hold here. And then once you have that, you might be able to quickly disengage if needed and get to your feet.
If you manage to get kani basami, but he gets up before you can get to a decent position, you can try transitioning to guard. Or you can try an oma plata by angling your body so that you're in a side by side position. As soon as he starts to sit up, you need to get your top leg out of there. Otherwise he can turn you over and take your back.
Just throwing out some ideas. Everyone has their own favorite techniques.
Hope that helps.
It depends on context.
The question is tagged "wrestling" and "groundwork" but, as others have pointed out, this move may not be "competition legal", depending on your rule set. By contrast, it is legal in many karate rule sets and, using your picture as the model, a left-legged kakato-geri (heel kick) would be an obvious choice.
There are two main followups one for each of two separate situations.
Competition: You move to a pin or a "ground and pound" position taking advantage of the fact that you can move on top of your opponent.
Everywhere else: Roll away and stand up quick. You don't want to be on the ground when his friends show up.
In situation 2 you actually probably did the variant where you are already prone at the start as opposed to choosing to go to ground.
From the perspective of Capoeira (my current style), during a typical exchange in the roda, if you've dumped the other person to the ground without touching it yourself with anything other than the allowed hands, feet, and head, you've already won the exchange, so you will typically either just extract yourself and help your opponent up, or mock a "ground and pound" attack against your "fallen" opponent. Some players will show a strike with the top leg to the head to indicate that they could continue capitalizing on the position.
In the case where they have caught themselves on the way down, and have landed in some sort of bridge or queda de quatro ("fall onto four", basically a crabwalk position), you typically either disengage, allowing your opponent to rise, indicating that you acknowledge that they caught themselves acceptably and that you want to return the game to a more upright position where you're not stuck in a test of strength (Capoeira, in general, discourages a lot of wrestling, and prefers moving to something new if the takedown doesn't work immediately), or you try to transition to another movement. From that position, the two most common continuations I've seen are to either twist the torso and then the legs to continue the rolling back, forcing the other player to try to do something to either reinforce their bridge or to continue to roll with the movement, or to extricate the bottom leg and to continue rolling into a shown kick to the head. I have, on occasion, seen someone instead going the other direction, kicking the leg underneath out to sweep the defending player's legs out to compromise their bridge in that direction, but at that point, you're also compromising your own balance, so it's more risky, plus you need to be careful about who you do it to, because if their shoulders are at an awkward angle, you can cause injury when they suddenly have their bodyweight solely on their hands.