If you have an NCO who clearly demonstrates incompetence as a leader, what are some tools and ways to relieve this NCO?

Counseling is easily the first and foremost thing that must be done! Remember that the counseling must be specific. Don't say 'you are a poor leader with no potential'. Instead, say 'on 8 May, you failed to ensure your Soldier's equipment was ready for Command Inspection'

Also, give them a plan of action. You cannot just tell someone that they suck and must fix themselves. You have to give them guidance on how to improve and then follow up to see that they performed the tasks you assigned.

If this all fails, then it is time to start looking at relief for cause or maybe even a reduction board.

BLUF: good thorough counseling is the key to quality control for ALL Soldiers.

I would like to combine the suggestions of MSG Stewart with that of MSG Quick. As MSG Stewart said we have a duty to develop leaders and guide them. I know it can be frustrating at times but that's what we do. The BAR to re enlist can be used as a very inspirational tool for someone to fix themselves, and is generally a quick fix. However, again, it has to be used properly, and the NCO needs to understand the bar completely. That will also require a formal counseling and breaking it down to them "barney style" if need be.

***EDIT*** Just wanted to add that one can overcome a bar to re enlist. Once it has been put in place, it can be removed later, if satisfactory performance/improvement has been met.

I will say ditto to all of the counseling advice and one more thing: deadlines. Ask for a specific performance objective (a training plan, or other basic MOS/NCO product) and set a deadline. Counsel again when he/she either requests an extension or blows the deadline (typically, I make them request the extension in writing and then I attach it to the counseling). Counsel again if the deadline is missed again or if the product is substandard (and attach the actual product).

If you are right, the Soldier will hang him/herself. If they have any desire for self-preservation, they will step up. Do not hide your motives; yes, I am building a packet. It's up to the Soldier to decide if I can. If I counsel and they give me the performance objective, on time, and it's excellent, what can I do? If s/he's as bad as you say, that won't happen.

Bar to reenlistment

Counsel, Counsel, Counsel! Document with facts not opinions, give him a chance to correct the matter throught the counseling, and then bring it higher with the packet in order.

I must agree with MSG(P)Quick Bar to Reenlistment. If you have been counseling the NCO the next step is to counsel the NCO about the Bar and send the up the chain of command. In the counseling inform the NCO why they are being recommended for Bar and both of you create a plan of action to remove the Bar after a preset date. The goal is to show the NCO his/her weakness and what can happen if they do not meet the standard. It will also shine some light on to the NCO with the Chain of Command.

Counseling, with aplan of action, complete the assessment portion of the counseling if he/she met or not the plan of action. I seen rehabilitate transfer to another section or unit sometimes it work, sometimes not, all depend on the person. But i.must agree with MSG Trod all counsel, counsel, counsel. Is the key.

Just because a NCO doesn't know his job doesn't make him toxic. Him not knowing his job and telling you how to do yours or doing the opposite of what he tells you might make him toxic. What says that he has not been doing special assignments? Drill SGT/AIT PLT SGT/Recruiter or just a job outside of his MOS...it happens. Alot of Soldiers slip through the cracks. Ones that should have been chaptered out but instead make it to the NCO ranks and then keep slipping. I know a few myself and they are horrible to work for. Do as I say and not as I do type people. Can't stand them but they are everywhere in the Army. Do your time and move on as the Army fails to try and remove people more than they use effort to remove someone.

Letter of concern after counseling has been initiated and completed with the after action review.
If NCO does not improve then best course if action is to notify the 1sg and have a letter of concern written up, my unit now has a 1sg that has done those actions before and he believes in it thoroughly
Airborne and good luck

Lead and guide them to competence. Their lack in competence does not negate your requirement to train and lead.
***edit***
I see that this view has already been mentioned.