The pieces, titled Head of Ali (1999), Solicitor’s Head (2003), and The Painter’s Doctor (2005-2006), were transferred to the nation in lieu of an inheritance tax bill.
They now form part of the museum’s extensive collection of more than 4,000 artworks, prints, sculptures, books and photographs.
This acquisition was made possible through the Arts Council’s Acceptance in Lieu scheme.
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Dr Emily Dunbar, curator and gallery manager, said: “We are delighted to acquire these prints with the generous support from the Arts Council.
“This is a major acquisition and will enable locals and visitors alike to see more works by leading British artists, such as Freud, for free in the Young Gallery.”
The three prints were from the estate of Lucian Freud and were accepted by HM Government in lieu of inheritance tax and allocated to The Young Gallery.
Michael Clarke CBE, chair of the Acceptance in Lieu Panel, said: “I am delighted that these three etchings by Lucian Freud have been allocated to the Young Gallery, Salisbury through the Acceptance in Lieu Scheme.
“The gallery’s print collection, which features the work of many modern British artists, will provide an excellent context.”
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These etchings, created by renowned artist Lucian Freud between 1999 and 2006, portray vivid portraits of individuals significant to Freud.
Head of Ali (1999) is a portrait of his son, Alexander Boyt; Solicitor’s Head (2003) is a depiction of Marilyn Gurland, a lawyer from Brighton, who approached Freud offering herself as a sitter.
The Painter’s Doctor (2005-2006) portrays Dr Michael Gormley, Freud’s physician and friend, who was also the brother of sculptor Anthony Gormley.
The three works will join the museum’s established collection of works on paper, which includes pieces by David Hockney, Henry Moore, John Constable and J M W Turner.
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The public will be able to view the three prints by Freud when they go on display from October 25 in Gallery 2.
Emmie Kell, director of Museums and Cultural Property at Arts Council England, said: “I’m delighted to see that, through the Acceptance in Lieu Scheme, the Young Gallery’s visitors will be able to enjoy newly accessible prints by one of the UK’s most recognised artists.”
Tim Chadsey, chair of the Supporters of the Young Gallery, said: “I am delighted that the Young Gallery was able to acquire these three etchings by Lucian Freud.
“Freud was an intense and challenging observer of the human form and I’m eagerly anticipating seeing them on display in the gallery.”