Tar-Minastir was the 11th ruler of Númenor, so named “because he built a high tower upon the hill of Oromet” (UT/220). His name might be a compound of a shortened form minas of minassë “tower” and a form of tir- “to watch”.
Quenya
Minastir
tower-watcher
minastir
masculine name. ?Watch Tower
Elements
Word Gloss minassë “fort, city (with a citadel and central watch tower)” tir- “to watch (over), guard, heed; to look (at), gaze, observe, to watch (over), guard, heed; to look (at), gaze, observe; [ᴱQ.] to keep, preserve”
Minastir masc. name, noun *"Tower-watcher" (Appendix A)