Digital transformation in the public sector provides digital services to the citizens aiming at increasing their quality of life, as well as the transparency and accountability of a public administration. Since adaptation to the citizens changing needs is central for its success, Agile methodologies seem best suited for the software development of digital services in that area. However, as well documented by an attempt to use Scrum for an important Public Administration in Italy, substantial modifications to standard Agile were needed, giving rise to a new proposal called improved Agile (in short, iAgile). Another notable example is the Scrum@IMI method developed by the City of Barcelona for the deployment of its digital services. However, given the importance of digital transformation in the public sector and the scarcity of efforts (documented in the scholarly literature) to effectively bring Agile within it, a strategically important contribution that Computer Science can offer is a general paradigm describing how to tailor Agile methodologies and, in particular, Scrum, for such a specific context. Our proposal, called Scrum@PA, addresses this strategic need. Based on it, a public administration has a technically sound avenue to follow to adopt Scrum rather than a generic set of guidelines as in the current state of the art. We show the validity of our proposal by describing how the quite successful Scrum@IMI approach can be derived from Scrum@PA. Although iAgile can also be derived from our paradigm, we have chosen Scrum@IMI as a pilot example since it is publicly available on GitHub.