Time and taste.
Appropriate volume.
Don't leave the bass player totally adrift when they're soloing.
I don't mind that so much from drummers (tho most will play something during a bass solo, just not much), but from the pianist, it's a killer. Sure, my soloing doesn't sound great with or without accompaniment, but without makes the bass solo different from the others, and I consider that a bad thing. I'll solo maybe once a set, if that, and I'd like for the overall vibe of the ensemble
not to be ... "and NOW --listen up, everyone-- we're gonna let the BASS player shine!". I get the lower volume thing which usually makes it necessary for the other musicians to bring it down a couple notches, but setting it out like that makes the bassist (and the solo) seem an accessory rather than simply an expression by another one of the musicians on stage.
Find some underutilized colours and use them. I've played with way too many drummers who never ride on closed hat. Backbeat on the HH column is cool too.
By "column", do you mean the HH stand or the rod the upper cymbal clamps to? I'll agree that riding the closed HH is rare (used to be a drummer in HS, not a great kit player, but it taught me to listen), and probably won't get much more popular in "jazz" because its straight-eighth presence in rock/pop/R&B/whatever kinda pigeonholes it as "not jazz drumming".
What I'd like? Well, if he's on stage, the timing and taste are a given. So I would prefer that drummers
not play the snare a lot on the 2 and 4. I mean, if the tune that's been called or is next on the list is that sort of tune, fine, but those tunes can be weeded out beforehand. The tunes I enjoy most call for something more fluid in terms of where he'd place accents and hits. No one (especially the drummer; it's so obvious) should be playing to remind anyone else where the beat is- they know, or ought to.
You haven't lived (or died a bit inside, your call)until you get on the stage with a guy from BigBandLand who "just never got into" a supreme artist like Tony Williams and plays
everything like the Rockettes are in front of him.