The footage shows Streep and director Phyllida Lloyd discussing the movie, and provides a first look at newcomer Alexandra Roach as a young Thatcher.
"There was a kind of earnestness about her that seemed entirely correct for the role," Lloyd said of Roach. "It was immensely important that the audience fell in love with the young Margaret and the young Dennis and believed that they are this young incarnation of their older selves."
The Iron Lady also stars Jim Broadbent as Denis Thatcher and Anthony Head as Geoffrey Howe. Lloyd previously defended Streep's performance in the film following criticism from former Conservative MP Norman Tebbit.
Broadbent described Streep as the "perfect " candidate to portray the former British prime minister.
The Iron Lady will open in cinemas on January 6.