In my experience teaching jazz, the left hand presents the most trouble for students. Applying chords at sight, at high speeds, in a creatively artistic way is the rub, as they say.
Therefore, with that in mind, I offer the following thoughts and exercises.
1. Spend most of your time on learning chords. Start with the 60 Jazz Chords. Learn the following in the 12 keys.
2. Drill Sonny’s thumbs around the circle of 5ths.
3. Drill the third/seventh combinations. Use blues then standard tunes to start.
4. Drill the rootless voicings.
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Remember chords are most frequently played by the left hand in the middle of the piano. The right hand often has to transpose the melody up an octave. The bassist covers the lower register.
Check out play along apps like iRealb to accompany yourself. It will supply a drummer and bass player for you. Click on the link for the app.