A source told ET last month that Markle is excited about her new Duchess role, and has been "anxious" to "jump in" and learn as much as possible about British life ever since she wed Prince Harry.
"She's ready to work as much as she can on as many projects as they will allow," the source said, adding that the royal family has been "impressed" with Markle's genuine desire to engage in charitable projects.
Since the May 19 wedding, the former actress has been accompanying the royal family to a number of public outings. One of her most recent appearances was at the Young Leader Awards reception at Buckingham Palace, where a source tells us she felt "completely at ease" with Her Royal Majesty.
"She has developed an increasingly close, warm relationship with [both] the queen and her father-in-law, Prince Charles," the source said. "She wants to please them and is doing whatever she can to educate herself to make sure she doesn't put a foot wrong."
Hear more on how Markle is adjusting to royal life in the video below.