How should the concrete anchoring some fenceposts relate to the driveway they're puncturing?
Since there will be now way to insure the concrete will be the same color or will it be able to tie in the texture to make the new pour "go away", neatly slope the concrete up towards the post say about a 1/2" to create a break line where the new concrete meets the old. Try to keep the slope uniform from post to post just so it will look professional. The slope will help drainage, even though the concrete acts like a huge sponge, holding moisture to the post, but it is much better than soil.

New concrete can smear over the old making a mess, but after a few hours, you can carefully clean the old concrete with a DAMP stiff bristle brush, no flowing water, taking MUCH care to not let the brush touch the fresh concrete. You may even wait 6 hrs and still accomplish this task.