I might be able to off some insight, based on two of my experiences --- IF I can explain things so they make sense to more than the neighborhood JackA**
Three of my horses have been together a minimum of 17-1/2 years. The strong Alpha and the Passive leader (happily second-in-command) have been together 20+ years. They were all geldings when I bought them.
I bought a long two year old colt in 2004. I kept him in a separate pasture until after I was able to get the vet here to geld him. I gave him a few more weeks of over-the-fence conversation, until he healed from the castration.
Everyone seemed to get along, over the fence but I still sensed something amiss with my strong alpha leader who, by 2006, was 19 years old.
I picked a nice quiet warm full of peaceful sunshine day to put Sultan in with the three old guys.
While things weren't peaceful, things weren't out of control ---- then all of a sudden they would get out of control and either the Alpha or horse #3 would be chasing the colt trying for all their worth to run him thru the fence
We have 23 acres so he had plenty of room to turn until I could get to him on the 4-wheeler.
I took to keeping him separated on the days I had to work and it was literally MONTHS before there was unsettled peace in the pasture. I bought Sultan in February and it was probably August before I felt I could breath when all of them were pastured together.
I studied them every day, trying to figure out the personality conflict. My best un-educated guess was that Sultan, the new kid, had somewhat of a dominant personality and while he wasn't really fighting my Alpha for total leadership, I would see him picking at my Alpha, safely testing the waters. When that happened my third in line (who was & still is the heir apparent to leadership because horse #2 doesn't want it), would go into Holy Fits and viciously tear after the colt.
It was a toss up who was more agile of the two and it was a comedy to watch as long as the fence wasn't part of the game.
I lost Sultan as a coming 4 yo to a freak pasture accident on a rainy day. It was about two weeks after the race horse, Barbaro's accident, when Sultan fell with a shattered front leg. Every bone between his ankle and knee was splintered. He is still here, below the barn, waiting for the others to join him someday. Hang in there, this is really is going to apply to your horses
On to the next #4 Horse, also a TWH, that I got sucked into buying by a friend who needed a little more cash to get her roof fixed.
Joker came to live with us about four months after Sultan's passing. He was the last horse in the pecking order at my friend's farm and has stayed the last horse on my farm. Joker has no desire whatsoever to climb over someone for herd leadership. He is perfectly content to let everyone else tell him what to do in an emergency.
The day I brought him home, I put him in the little pasture in front of the house so I could watch everyone introduce themselves and talk.
Something about my alpha's body language and way of talking made me think he actually liked and would quickly accept Joker. My horses always come in at night, so everyone had stall time to get acquainted and the very next day I turned Joker out with everyone.
To my astonishment there was no squealing, no kicking, no nothing, except "it's time to head for pasture, you stay in the back and do what we say".
That was seven years ago and things have stayed peaceful, except for those times Horse #3 decides his bullying self wants to make trouble; it's just who he is. He just seems driven to steal someone's lunch money a few times a month.
My point to that long, drawn out story, is that I'm pretty sure it's your new horse sending vibes to your alpha that the alpha isn't appreciative of.
Sooner or later they will come to terms but these are probably going to be two horses that will always need watched, so nobody gets hurt.
IMHO, it would not be a good thing to take either of them on a week's horse back vacation without the other. I'd bet money they would be right back to square one when it comes to fighting.
I hope that all made sense and is of some help