I have trouble playing the Gmaj7 chord with my left hand. I'm using 5-3-2-1 fingering, but I can't avoid hitting the A key with my 4th finger.
What exercises or techniques are used to void that?
Try shifting your hand toward the fall board (i.e., away from your body). That will bring your thumb closer to the F#, allowing additional relaxation in the rest of your hand.
So this:
Rather than this:
Make sure your fingers are curved not flat. Maybe they need to be further forward on the keys.
Play down the Gmaj7 chord. Keep the notes held down, play a series of A notes with your 4th finger. You'll find it pretty tricky! Try not to lock your hand - relax! But it will teach you to lift that finger independently.
Consider rootless voicings -- start on F#, then B and D (or voice it B,D,F#, that works too).
http://www.thejazzpianosite.com/jazz-piano-lessons/jazz-chord-voicings/rootless-voicings/