There is currently temporary exhibitions, about circus at Western bank (within Sheffield university) and Western Park Museum.
As this extract from article about Western bank exhibition explains, this year marks the 250th anniversary of what is considered to be the birth of circus in Britain.
n 1768 in London Phillip Astley unveiled a show which, for the very first time, combined equestrianism, clowning and acrobatics within a now iconic circular ring. This ground-breaking performance marked the birth of a global phenomenon; 250 years later, circus continues to amaze and astound audiences, showcasing the talents of legions of impossibly skilled performers in shows around the world.
I have been to the Western Park exhibition. There is circus posters, exhibits about different performers, stuffed circus animals and a canal skeleton. There are two screens, showing films. When I was there one screen was showing acrobats and other women with circus connections discussing circus. Additionally there are dressing up clothes for children. I have pictures on my Wonderwall360 instragram of a couple of the exhibits.
In a slight derivation to circus, Kelham Island Museum has archive of fairground memorabilia.