As others have stated above, probably the best way to do this would be to keep the Bolsheviks occupied elsewhere, either through a protracted civil war that would allow Turkestan to consolidate and strenghten itself or through the defeat of the Bolsheviks themselves.
There were no "other" side in Civil War who could let Turkestan go. Whites would be even quicker in re-establishing control.
I don't see much chance of this new Turkestan surviving against a unified new Russian empire, be it Bolshevik, White or otherwise-for Turkestan to survive, we need a divided Russia.
Not just Russian Empire, but it's any part bordering Turkestan would be enough to exterminate all possible Envers there. IOTL Turkestan wasn't primary, secondary or even tertiary theater of war - it was forgotten periphery and Bolsheviks won there with bits and pieces they could scrap (although they had very capable top general, M. Frunze). So, anything more than 1/5 of IOTL Russian Federation would have enoough military power to deal with Enver.
So you would have the Russian Civil War turn against the Bolsheviks, perhaps through White victories that resulted in a partitioned European Russia or nationalist revolts that keep places like the Ukraine, Georgia and Azerbaijan independent.
Azerbaijan put up as much fight as it possibly could, Georgia (for all today's bluff about Red Conquest) and Armenia made a choice between becoming read or becoming dead (Kemalists were advancing).
As well, Turkestan could look elsewhere for benefactors in a number of scenarios. If you did this in a TL where the Central Powers won, they could look to Germany.
So basically, Enver himself has no role as history-maker, it is that certain combination of stars could make Turkestan independent. Yes, this is plausible scenario (after all, it describes OTL 'Stans suddenly becoming independent in 1991), but what does it have to do with Enver???
I would also wonder about the health of Enver's Turkestan long-term. I would see the supporters of the Basmachi Revolt as more conservative, more in line with traditional Islam. Give them a decade or two in power and perhaps more reform-minded, modernist Muslims overthrow the government. Or a military coup by Ataturk-like officers from the large army that Turkestan would have to create to protect itself from its neighbors.
You hinted on perennial problem of this ASBish creation - it is absolutely devoid of loyal educated class. Whatever indigenous educated group Turkestan did possess, they were leaning toward Russia, if they weren't outright Bolsheviks. Enver could import Turks, but that would likely create all sorts of frictions between Turks and Uzbeks (and don't get me started on feelings of Iranian-speaking population, which included majority of urban population and tradesmen).
Fun scenario: An earlier Afghanistan-style war, say in the 40s or 50s, where a smaller Soviet Union/revived Russian empire attempts to invade and take over an independent Turkestan. They win militarily but then are bogged down in a decade-long guerilla campaign that turns into a jihad and their ultimate defeat.
This is pretty much IOTL description of Western Ukraine in 1945-1955, but guerillas can't inflict Afghanistan-comparable losses on regular army of the day in arid country before RPG and Stinger become ubiquitous. Shturmoviks will hunt guerillas down and turn them into mincemeat.
In this period the Kemalist regime was fairly friendly with the Soviets, so there's no question of Enver getting any assistance or even good will from the Turkish government.
C'mon, Enver was bloody
sent by Reds to Turkestan, he was their best friend. I have no doubt that, would his hare-brained plan work, he would have no problem securing alliance with Kemal if Kemal would see it as beneficial.
The backwardness is a defense as well. One of the principal reasons why the Ottoman Empire survived is that the amount of troops Russia could attack it with were severely limited by logistics.
Yes, but Turkestan had several railroads crisscrossing it at this point and, once built, railroad is pretty hard to demolish completely. So I wouldn't bet on Enver's ability to hold Northern Turkestan (basically anything north of Pamir).
Likewise, the ability of the Red Army to operate in large numbers in the far reaches of Turkistan are limited. The Red Army is not as impressive in this period as you may be building it up to be. Poland kicked it's ass.
Well, it isn't superb, but local recruitment base Enver could rely on is absolutely miserable. So, it isn't question of Red Army's strength, it is Enver's built-in weakness.
Likewise, Enver and his cadre of veteran officers were capable of developing (and did) an efficient fighting force.
Successfull gang completely destroyed by SINGLE cavalry brigade. There's a difference between this type of force and anything capable of establishing permanent control over a region. Somebody should fire field pieces, built fortifications, establish field signal system. Where would Enver get those specialists?
The area Enver controlled were hard to reach and impossible to cut off the supply to arms to. There's no question that a concerted effort by the USSR would be successful, but I'm not convinced that this would necessarily be forthcoming. The USSR was content to give up a lot of territory to Poland, etc., and there are too many things to worry about to be futzing around in the middle of nowhere. Even in OTL it took four years after Enver was killed to defeat the Basmachi Revolt.
If Enver had set realistic goals and played a smarter game diplomatically, something could possibly have been retrieved.
So, you're talking tiny little chieftaindom, forgotten among some of tallest mountains on Earth and playing very nice and friendly with neighbouring Soviet Turkestan (to avoid devastating punitive expedition it couldn't protect itself against), aren't you? That MIGHT fly, but why did you call it "Turkestan"?