"Director nomination" refers to the process of selecting or proposing someone as a candidate for a board of directors position in an organization. Full definition
I wouldn't be surprised if it gets a Best Picture and Best Director nomination as well. (incontention.com)
All four of those movies earned corresponding Best Director nominations. (decider.com)
While Vidor's career continued well into the talkies — receiving Best Director nominations for «Hallelujah» (1929), «The Champ» (1932), «The Citadel» (1939) and «War and Peace» (1957)-- he was most closely associated with, and celebrated for, the great filmmaking of the late Silent film era. (indiewire.com)