From *ad-(“to seperate”) + *-ïr-, the root is not attested on its own.
Some like Erdal and Nişanyan suggest *ādïl-(“to sober”) and *ādïg(“sober”) are derived from the same root as well[1],[2] however some reconstruct an alternative *ād-(“to sober”) root on the bases of Turkishaymak, however that verb is attested at a very late date and may be a back-formation.
Clauson suggests *üdür-(“to choose; to separate, scatter”) is a variant of this verb, however this is unlikely from a phonological standpoint.
^ Sanžejev, G. D., Orlovskaja, M. N., Ševernina, Z. V. (2015) Etimologičeskij slovarʹ mongolʹskix jazykov: v 3 t. [Etymological dictionary of Mongolic languages: in 3 vols.] (in Russian), volume I, Moscow: Institute of Oriental Studies of the Russian Academy of Sciences, page 42
Clauson, Gerard (1972) “aḏır-”, in An Etymological Dictionary of pre-thirteenth-century Turkish, Oxford: Clarendon Press, page 66
Sevortjan, E. V. (1974) Etimologičeskij slovarʹ tjurkskix jazykov [Etymological Dictionary of Turkic Languages] (in Russian), volume I, Moscow: Nauka, page 114
Räsänen, Martti (1969) Versuch eines etymologischen Wörterbuchs der Türksprachen (in German), Helsinki: Suomalais-ugrilainen seura, page 6
Starostin, Sergei, Dybo, Anna, Mudrak, Oleg (2003) “*adɨ-r-”, in Etymological dictionary of the Altaic languages (Handbuch der Orientalistik; VIII.8)[2], Leiden, New York, Köln: E.J. Brill