after he puts the hill inside his legs and pushes the knee, left hand is basically free to do what you want.. hold opponent's right arm, so he won't post and get swept more esily, for example. 

I am not really sure who you are refering to, so I will give both views.

The top guy uses his right hand to block the hip. I personally prefer to post my hand next to hip to prevent the hip escape, but whatever works best for the situation is ok.

The top guy should use his left hand to control the opponent's right arm, but might need to use it for controlling the left arm. All the while probably trying to control the head. (which is not easy when you want to keep this position statically)

The bottom guy will use his right hand to defend his neck and can use it to help blocking/lifting the shin of the opponents right leg.

The bottom guy will use his left hand to control the shin of the top guy (on the inside). I think the most important part, is to keep the left arm close to the body, there should be no space inbetween the bottom guy's left arm and body (to prevent armbar attacks).

I think the key to the escape is the fact that you control the shin of the opponent before bridging and then 'hold it in the air' while you come back from your bridge. This will create a small gap underneath which you can use to continue into a hipescape and get the half-guard. Doing this holding with your right hand is easier but leaves your neck more vulnerable. In the video Comprido uses both hands which is the most easy to escape.

Hope I didn't mix left and right somewhere... 

Thank you Ken.