Though “tenure” and “tether” have no etymologically common roots, I am a poet, and so I think of words in associations made through use, sound, image, etc.
According to the online etymology dictionary of Oxford English, here are the quick synopses of the roots of the two words.
early 15c., “holding of a tenement,” from Anglo-French and Old French tenure “a tenure, estate in land” (13c.), from Old French tenir “to hold,” from Vulgar Latin *tenire, from Latin tenere “to hold” (see tenet). The sense of “condition or fact of holding a status, position, or occupation” is first attested 1590s. Meaning “guaranteed tenure of office” (usually at a university or school) is recorded from 1957. Related: Tenured (1961).
late 14c. (implied in tethering), “confine by a tether,” originally of grazing animals, from tether (n.). Figurative use also from late 14c. Related: Tethered.
late 14c., “rope for fastening an animal,” not found in Old English, probably from a Scandinavian source akin to Old Norse tjoðr “tether,” from Proto-Germanic *teudran (source also of Danish tøir, Old Swedish tiuther, Swedish tjuder, Old Frisian tiader, Middle Dutch tuder, Dutch tuier “line, rope,” Old High German zeotar “pole of a cart”), from PIE root *deu- “to fasten” + instrumentive suffix *-tro-. Figurative sense of “measure of one’s limitations” is attested from 1570s.
Perhaps there is something to be said of the connection between the two words. “Tether” can be sourced to the late 14th century, while “tenure” is first seen in the early 15th century. There isn’t too much distance in time, but there is an extreme difference in power. “Tenure” is associated with right, the holding of a status from a stance of authority, while “tethering” is connected with an animal fastening through rope. The animal has been controlled by another person’s dominant act of asserting a rope around its body. If used in the figurative sense, as indicated above, the “tether” reveals “one’s limitations”, but I believe that it goes beyond that.