The front squat – push press is a hybrid exercise that combines the front squat and push press into a single movement. Note that this is not the same thing as a front squat + push press, which is a complex of two distinct movements.
 
Perform a front squat with as close to your jerk rack position as you’re able to, and accelerate up as much as possible. As you reach the top, continue driving up into a push press.
 
In other words, simply perform a push press with a full squat as the dip.
 
Notes
If you’re unable to front squat with a jerk rack position, get as close as possible, and shift the position as you reach the top of the squat so you’re able to transition smoothly into the pressing motion.  
 
Purpose
This exercise can be used to train better recovery speed and posture in the front squat and clean, although because the weights are lighter than with a front squat – jerk, the effect is limited. It’s more often useful as a warm-up for the jerk that simultaneously helps front squat/clean posture and recovery speed.
 
Programming
Sets of 1-5 reps are suggested with weights anywhere from 50% to the lifter’s maximum push press. Generally this exercise should be performed following any snatch variants and possibly before clean variants depending on what the intended emphasis of the workout is.    
 
Variations
This movement can also be performed as a back squat with a push press behind the neck with either a jerk or snatch grip.