Tenure is a permanent academic position. The position is very safe, as it is far more complicated to fire a tenured professor than an employee who has a permanent contract. There are variations, and for example in Finland there is no "true tenure": permanent professors have as much job security as a permanent plumber. If you want definiteness, you can restrict this question to tenure as understood in most of the US today. Is there a good Latin word or phrase for "tenure" or "tenured" that would capture the sense of permanence and immutability?
In Italy, quoting the website of the European University Institute,
apart from ‘assegno di ricerca’, ‘professore a contratto’, and ‘ricercatore di tipo B’, all other positions are tenure or tenure-track.
In particular any position of Associate Professor (‘professore associato’) is a tenure-track or tenured one, and that of Full Professor (‘professore ordinario’) is tenured after a probationary period ('professore straordinario').
We may generalise saying that "tenure" (somewhat if not perfectly) corresponds to titolarità di cattedra, and is usually translated as such - literally "ownership of a professorship chair". Since titularis is an attested Late Latin word, we may translate tenure as titularitas cathedrae. This German website describes Paul Fridolin Kehr as titularis cathedrae historiae medii aevi Gottingensis, so "tenured professor" may be translated as (professor/docens) titularis cathedrae.
To make sure the word is understood correctly as referring to the academic concept of tenure, I suggest taking a word that is easily connected to the English "tenure". My suggestion is tentura, "holding" (roughly), from the past participle tentus of tenere, "to hold, master, guard, or stay". I think this captures the idea quite nicely is easy to recognize.
The derivation of tentura < tenere is similar to censura < censere and cultura < colere; it should not be confused with a future participle. For a comparison of the two, see this question on whether cultura is a future participle.
Central-European have a similar concept where the important step is a habilitation. habilitatio (medieval) - making qualified or eligible, declaratio habilitatis - declaration of qualification. After a habilitation one becomes a docent - docens - teaching (a lecturer).
The closest Latin word in meaning is probably immobilis, 'immoveable, unalterable' — though it is usually applied to some physical entity. However, if that isn't acceptable, then indemobilis might be reasonably derived from the verb demoveo, which can certainly be applied to individuals.
[Such positions are found in England, defending against dismissal in all but extreme circumstances, but there's no general rule about them. The principle still seems to be applied in some universities, but not nowadays in the Civil Service, which until a few decades ago spoke of officers not as tenured, but 'with establishment'.]