Good advice from someone with firsthand experience clear coating the binding. However I'll just add one thing relative Mark's final comment.

A slight amount of stain will be picked up and dragged about in the clear coat. Let it dry.
Now is a good time to give the binding a good scrape with a shape blade as the colour is sealed in and no more will drag across the binding leaving a nice clean finish (We hope).
This is only relevant presuming you're going to do a hand-applied finish like wipe-on poly or Tru Oil etc.
If you're spraying your clear coat, the stain will not move unless you spray it too heavily and get a run, then that may be enough to attach itself to the clear and create a problem.

So if spraying, do a couple of very light might coats first, allow them to dry and follow with "normal" coats. This will "set" the stain as well as provide better adhesion for subsequent coats.