Get a smooth sound. If you're like most jazz bands, you'll be providing smooth, cool music, sometimes as background or a stage act but always sophisticated. A guitar with gain or distortion can ruin your act. In jazz guitar, you have to be able to hear the strings.
Get to know the fretboard really well. Practicing scales helps a lot. You should be able to find "keys" so that when the band leader (lead vocalist) calls them out, you can follow.
Find out what chord types mean. Chords like "augmented fifths" or "sustained" chords are just names for regular chords with a note or two added. You don't have to be a chord expert, but getting beyond G and C major will help your jazz career.
Go beyond chromatic and pentatonic scales. You can use these scales as a basis for your work, but for jazz guitar, other notes should be added. The jazz guitarist dances a thin line between innovation and dissonance: Potentially dissonant notes, added in the right places, enhance a jazz riff.
Get "stock jazz" phrases. For example, instead of going up from A to B to resolve on B, try a three-note climb from A to A-Sharp/B-Flat and then to B. The sound will be a "da-da-da" sliding upward to end on the B note. Use stock riffs like this one to jazz your guitar.