Gaspari was born in Gissi, in Abruzzo, a region which would be his main electoral basin during his political career.
Gaspari was a member of the Italian parliament without interruptions from 1968 to 1992.
He was a member of the so-called Dorotei wing of Italian Christian Democracy (Italian: Democrazia Cristiana, simply DC) along with Vincenzo Scotti, Arnaldo Forlani and Antonio Gava.
After a period as Minister for Mezzogiorno, he ended his government career as Minister of Public Functions in the sixth and seventh cabinets led by Giulio Andreotti in the early 1990s.
A song by Elio e le Storie Tese mentions an episode in which Gaspari used a state helicopter to arrive in time to watch an AS Roma football match.