Aylett is best known for his career as an administrator in the 1970s and 1980s. He was elected to the position of North Melbourne Football Club president in 1971, and his innovative off-field leadership in securing sponsorship and running corporate entertainment – including the rise of the North Melbourne Grand Final Breakfast as one of the Grand Final's most prominent events – followed by his aggressive recruitment of star players, particularly through the use of the short-lived "ten year rule" in 1973, turned North Melbourne from perennial also-rans to a professionally run powerhouse of the 1970s, and the club contested four consecutive Grand Finals between 1975 and 1978, winning two.
In 1977, Aylett was elected president of the VFL. He continued his aggressive efforts to push the game's administration towards professional and business-driven success. His actions in setting up the VFL's Night Series in 1977, as a direct rival to the NFL's Night Series, delivered both sponsorship opportunities and laid the platform for the VFL to supersede the NFL for control of football in Australia. Under his guidance, the league expanded into the Sydney market, making preparations for an expansion team before South Melbourne opted to relocate there; Aylett subsequently sat on the Swans' board of directors. Additionally, during his tenure, the VFL began to establish regular Sunday matches in Victoria; and he fought the Melbourne Cricket Club and the Victorian Government to move the Grand Final to VFL Park, ultimately failing to make the move, but securing a better financial deal for the VFL and better ticket access for VFL members. Aylett stepped down in December 1984 following the establishment of the VFL Commission. Aylett also served as president of the National Football League from 1978 until 1985.
Aylett signalled the end of his administration career after a final stint as North Melbourne Kangaroos president from 2001–2005.