The streaming service posted the image with little fanfare on its UK Twitter account, captioned with the word "patience". Olivia had earlier said in a statement about portraying the Queen in the show.
In the screen shot Elizabeth is drinking a cup of tea, and appears to be taking breakfast in the Palace.
Coleman has said she is "thrilled" to take on the role, and has called her predecessor Foy "a real genius" and "an incredibly hard act to follow".
The actress added that she'll most miss "the people making" "The Crown".
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Foy, 33, who earned a best actress Golden Globe for her portrayal of the Queen a year ago, has previously said she will "miss the role terribly".
"Watching the first series was blissful because I had no idea". The show is also set to cover Prince Charles' marriage to Princess Diana and his subsequent affair with Camilla Parker-Bowles - now the Duchess of Cornwall - and the Margaret Thatcher era. Matt Smith, who played the queen's husband in the first two seasons, will not reprise his role on Season 3 either; Tobias Menzies will play a middle-aged Prince Philip instead. Based on the award-winning play, "The Audience", the series reunites creator/writer Peter Morgan (The Queen, Frost/Nixon) with director Stephen Daldry (Billy Elliot, The Hours) and producer Andy Harries (The Queen).
However, since they're loosely following history, series three will see the monarch cultivate her steadiest relationship with Prime Minister Harold Wilson, who served as head of the British government during this period. Actor Josh O'Connor ("God's Own Country") has been rumored as a strong candidate.