He then did pastoral work in Imola until 1931, and furthered his studies at the Pontifical Roman Athenaeum Saint Apollinare in Rome, from where he obtained a doctorate in canon and civil law in 1933.

He received his episcopal consecration on the following 28 October from Pope John XXIII, with Archbishop Diego Venini and Bishop Benigno Carrara serving as co-consecrators, in St. Peter's Basilica.

Pope Paul VI, whose reign Staffa predicted to be "truly great",[1] later named him as pro-prefect of the Apostolic Signatura on 7 April 1967, and created him cardinal priest of S. Cuore di Cristo Re in the consistory of 26 June 1967.

[2] Staffa was made cardinal priest of Santa Maria sopra Minerva on 24 May 1976 and later died in Rome seven days short of his 71st birthday.

The archbishop was believed to have written a decree issued by his congregation on 25 May 1963 that demanded that Catholic universities receive the Vatican's approval before awarding honorary degrees.