One of the goals as a drummer should be, in my opinion, to achieve a certain sense of unity and balance between all parts of the drum set. This is often easier said than done!
These are a couple of comping exercises that I've been messing around with. These have helped me towards developing a deeper sense of time and a unified sense of 4-way coordination.
Play both of these examples with the standard ride cymbal beat:
Rhythmically, both of these phrases are a series of syncopated, poly-rhythmic eighth-note figures that create an over-the-bar-line loop. This is challenging enough on its own, playing these figures with just one limb against the ride cymbal beat (for what's it's worth, this eighth-note figure was inspired by some Alan Dawson concepts I came across. You should practice this too!) but my exercise splits the rhythm in a sequence between the snare, bass drum and hi-hat.
The order of the orchestration between the snare, bass drum and hi-hat isn't by accident either and intentionally by design. I won't spoil it for you so play through these two examples and see if you can figure out the logic of each pattern.
I've also found this to be a helpful way to incorporate the hi-hat into my comping phrases (i.e. Roy Haynes).
Play it slow.
Balance the limbs dynamically.
Use a metronome.
Relax and strive for a sense of flow.
Make it swing!
* If you have any questions please let me know!*