John Wayne ----> Dennis Hopper (True Grit (1969).)
Dennis Hopper ----> Glen Morshowser (24, Season 1.)
Glen Morshowser ----> Patrick Stewart (TNG, Season 2, "Peak Performance.")
Patrick Stewart ----> Leonard Nimoy (TNG, Season 5, "Unification I/II.")
Leonard Nimoy ----> William Shatner (TOS Series and Related Movies.)
EDIT. Movies only?! That strikes me as too limiting, but whatever.
John Wayne ----> Dennis Hopper (True Grit (1969).)
Dennis Hopper ----> Sandra Bullock (Speed.)
Sandra Bullock ----> William Shatner (Miss Congeniality.)
(Which actually got it done quicker, I guess, without having to think along a "Star Trek" connection. Still, Shatner has more TV work than film work, meh. Whatever.)
Bradley Cooper