I want an intra-post transfer. How can I accomplish that?

You're getting a lot of advice here that may seem contradictory at first so let me explain the overarching picture so that it all ties together, and I will explain why I recommend against chasing the IPT down the rabbit hole.

Every transfer requires the approval of the higher command. There needs to be a reason, and the approval of higher. If you want to transfer companies, the battalion must approve. To transfer battalions, the brigade must approve. Brigades, the Division approves. Divisions, the Corps approves. I don't think there are any posts with two separate Corps, so that is moot. If you want to transfer MACOM, HRC must approve. That is your branch manager. When you are looking at a unit to transfer on post, it matters what your highest shared command is. No matter what anyone tells you, what letters of acceptance or release you may have, only your branch manager can move you from one MACOM to another, even if it's two blocks down the street. Those assignment instructions must come from HRC, and anyone who promises to move you without the branch manager to another battalion in another MACOM is blissfully unaware or flat out lying.

Second part is the reason. Why are they asking to move you? If you want to move companies, your 1SG has to get with the other 1SG within the battalion and the battalion moves you. Lets say you want to move to a different battalion within the same division. Your CSM talks to the BDE CSM who talks to the BDE CSM in the other brigade. The division approves the move. But why should he move you? What is the justification to move you? Sometimes when people are in their reenlistment window a CSM will offer to move someone who wants to move but stay on post. That's a drug deal they ware willing to make. If you want to switch MACOM's, go to a BCT in a FORSCOM unit, or a SF Group assignment, or work at a hospital, or an AMEDD assignment, HRC has to approve the move. They have time on station rules that can only be broken with an exception to policy. Exceptions are for exceptional cases. Unless you are getting a compassionate move because you need to take care of your dying wife, or you are the victim of a sexual assault from someone within your unit, your case is not exceptional enough for HRC to break its time on station rules.
While you can approach your CSM to move, you need to picture how that conversation will go. Why do you want to go? Your career progression? Well, they will have a serious conversation about how you can be learning your job, the Army, leadership, and progressing your career in your current station. Is it because you are exceptional? Why would they want to trade you away then? You're asking a CSM to trade away a known value for an unknown value. They don't know what type of person the other unit will give away. No unit wants to give away a good Soldier. Plus they have to find another Soldier from the unit you want to go to, same rank, who wants to go where you are.

What usually happens in these IPT's is that the Soldier approaches the 1SG or CSM about the request. They tell the SM they will look into it. It turns out to be a lot more work than it's worth, or they don't get an answer in a timely manner. Months go by and one of the two SM is still waiting on a letter of release from some general, or it just got put on the back burner, or no one volunteers to move. Now, the Soldier has wasted months of valuable time and is more disillusioned because they feel the leadership led them on and failed to come through for them.

So, can you ITP? Absolutely. Will you? In most likelihood, in your situation, you will not. Your time is better spent pursuing efforts more likely to come to fruition, or invest your time in your current location wisely by concentrating on self development until you can move.

Talk to your Div CM SGM, they may be able to help you out. But you better have your stuff together. Give them a call, have talking points, fresh haircut, uniform strac, love me book (PT, weapons, certs), and know where you'd like to go. Ensure you have permission to go.

There are two things you can do, you can contact your branch manager to see if there are any available slots on your current installation for your grade. The second option is you can inquire from other organizations on the installation to see if they are in need of and have any slots for your MOS. If they do you will have to schedule an appointment with that Battalion CSM to talk with him about getting a letter of acceptance from him/her to be assigned to their unit. If they do this, you would have to get a letter of release from your current Battalion, which mean you would have to talk with your CSM as well. Both Battalions would have to be in agreement with the transfer. The draw back to this is, some Battalions won’t do a leeteyof release unless they can get another Soldier from the Battalion that’s accepting you. However, it won’t hurt to try this approach especially if you’re trying to stay at your current installation. Good luck to you...

Just saw you're a CBRN Soldier in CBRN unit, and a TE unit, at that.
I'm going to offer you some advice from an old Chem Dawg.
Chemical Soldiers fight, and wait, and fight, and wait, to get in a Chem unit. I didn't look at your profile close, and was thinking you were running an NBC room somewhere, which can sour someone because you really don't have good guidance and you get stuck doing a bunch of nonChem things. You've hit the jackpot, and want to move.
Disregard my earlier advice to go see the Div CBRN SGM, and disregard anyone else's advice to go see any CSM about moving. You can disregard that, and they'll likely take the next inbound 74D headed to an IN or FA unit, and give you that transfer you believe you want. Then, you'll understand not getting anywhere in your career because they are going to take care of their folks.

If you don't have L3, compete to get it. If you have L3, you are where you need to be, and your only options are those given by SFC Boyd. Keep in mind, if you're not scoring 270 or above on your worst APFT, you need to work on that between now and any attempt at SFAS or Ranger options.

Submit a 4187 and see what happens.

Submit a 4187 soldier action request form, a 368, a letter of why you are wanting to go Active submit that to your Readiness NCO and it will go up the chain all the way up to your State TAG for sign off once that is complete, you will be already be meeting with your Acrive Duty Recruiter to see what jobs that Mother Army Needs you for. In the meantime the Recruiter will start their process of getting you into Active Duty via application SF86 OPAT test, new ACFT test, physicals etc.

The Army Times used to publish ‘desired transfers to?’ and others wanting to switch could respond.

There is no longer a medium for wanna do transfers and such switches of duty stations? SPC (Join to see)

Basically, you can't. An interpost transfer is not something you get to request, it is a tool used for specific circumstances. As for a 4187, that is a request form, not a magic star cluster. It is a form used to request something that is already authorized. It must be addressed to a specific person asking for a specific thing. When interpost transfers are conducted, someone at a higher level has already worked out there is a hole to fill and designates the person to fill it. This person is usually strength management.
You said you have 2 years left on your contract? In a little over a year you can reenlist for a different duty station that will probably have a report date of a year after that. So, you can stay there two years and ETS or stay there two years and PCS.
If moving is really that important to you request airborne training from your branch and PCS or go to Psyops, CA, SF, Ranger, or 160th selection and you will PCS. There are plenty of ways to advance your career, you just have to be willing to work for them. You could easily be advancing your career by working on college which would separate you from your peers once you are competing for Senior NCO promotions.

How long ago was it that you graduated AIT?