Beginning with a solid fundamental hip switch position (more on this below), your intention is to wait for your partner to try for an underhook, one of the most common reactions you'll encounter from half guard), and use this to catch the Kimura. However, your partner has cleverly wised up and hidden their arm behind your head. In the above video, Vince puts his right arm around my neck and hugs it tight, even turning his thumb toward him in order to avoid opening his elbow any. His defense is very tight. Typically, when catching the Kimura, you want to slide your far arm (left, in this case) through your partner's elbow, but because of the defense, use your right hand to fish through their elbow and on to the other side (the gap on this side will be considerably larger). Once you've created the space, you can slide your hand down to their wrist, ultimately straightening their arm and making it considerably easier to catch the Kimura.