Rex Brewster is a character created for the 1982 film Evil Under the Sun. He shares the same last name as the character Emily Brewster, from the original novel but has an entirely different back story and plays slightly different roles in the plot.
Unlike the original Emily Brewster who is an athletic woman and rowing enthusiast, here Rew Brewster is a writer and a theatre columnist. He has written a biography of Arlena Marshall and needs her release so that he can publish it. However, Arlena refuses. Rex is upset and at one point threatened Arlena, making him a plausible suspect in her subsequent murder.
In the original, Emily had a natural alibi because she rowed into "Pixy Cove" with Patrick Redfern and discovered Arlena's body. In the adaptation, Rex's alibi is establihsed a different way. He was not with Patrick Redfern and did not discover the body. He was in a paddle boat but never went to "Ladder Bay" where the body was found. Around the time of the murder, he was in his boat and met Linda Marshall who was swimming in Gull Cove which was far from Ladder Bay. Linda supplied his alibi.
However, Rex and Emily do have the same plot role in one respect--both experienced a bottle being thrown at them. In the case of Rex, he was in his paddle boat when a bottle, apparently thrown from a cliff above, landed in the water near him.
Rex Brewster is portrayed by Roddy McDowall.