Pull your ribs up.

With the weight of the bar pinning you to the bench, lift your rib cage toward the bar. This will improve leverage and stability.
Lift your rib cage
Push your chest up as much as possible like you're trying to touch your chest to the barbell
Barbell Medicine
An effective cue for this is to "show off the chest" just like in the deadlift. The thoracic erectors arch the upper back to give the chest muscles better lines of action to the upper arms.
Starting Strength
...think about bringing your chest to the bar instead of the bar to your chest.
Lift your chest and lats while leaving your hips down. Try to spread your chest up to the bar, and use the appropriate leg action based on your foot position to keep your butt glued to the bench.
As you descend continue to pull your ribs up hard to meet the bar...you NEED to actively push your ribs towards the bar during the ENTIRE MOVEMENT.
MPS Training
Improve leverage and stability
I want you to think about bringing your chest to the bar... That's going to keep your upper back tight and extended and that's gonna keep your lats tight.
Alan Thrall
Reactive Training Systems
As she brings down brings the bar down, we're trying to reach up to the bar with her chest...It's become a very common practice for athletes to lift their head off the bench, and unless you're very very mindful of it, then as the head comes up, the chest will often come down and the chest will sort of retreat from the bar and that can cause a loss of upper back positioning. It can cause a loss of tension. It's also going to cause you to have to move the bar a further distance... You shouldn't need to lift your head...just be mindful of keeping your chest as high as possible throughout the lift.
By throwing your chest up, you put the bench movement further up your shoulders for more leverage. Chest up, shoulders back.
Once I’m lowering the bar, I try to bring my belly up to the bar to meet it. This not only keeps my arch solid but also keeps my upper back locked in.
As you lower the bar, actively drive your chest up to meet it to slightly reduce range of motion.
Stronger By Science