Up until this point, Meghan has always been accompanied by her husband Prince Harry or another member of the household.
The Duchess was taken on a tour of the exhibition, which marks the 250th anniversary of the Royal Academy, founded in 1768 – the same year Captain James Cook set out on his first Endeavour expedition.
It brings together around 200 exceptional works from public collections worldwide, and spans over 500 years.
It includes artefacts from different regions, including New Zealand, Australia, Fiji and Tonga, which the Duke and Duchess will visit on their royal tour in October.
Meghan also met with the curators and artists as well as descendants linked to the works displayed and watched a short performance from Ngāti Rānana, a Māori cultural group.
Last week, the Duchess announced her first charity project, supporting a cookbook with the Hubb Community Kitchen, who have been affected by the Grenfell Tower fire.
She was joined at the launch by Prince Harry and her mother Doria Ragland.
On Monday, Harry and Meghan attended the Coach Core awards at Loughborough University, where they met with graduates from the programme.
The pair competed against each other in a netball workshop but there were no hard feelings shown as Harry’s team won – the pair shared a cosy cuddle.
September 25 is also of special significance for the couple, as it marks one year since the pair stepped out in public together for the first time at the Invictus Games in Toronto.
Just a couple of months later, the pair announced their engagement and they married at St George’s Chapel in Windsor, on May 19, earlier this year.
‘Oceania’ will run at the Royal Academy of Arts from 29th September – 10th December 2018. For more information about the exhibition visit royalacademy.org.uk/exhibition/oceania
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