The Director has apparently been around since the 1940s. Despite that, he appears to be in his 40s. He is trusted by the President of the U.S. and Coulson, and they both approved his promotion to Director of S.H.I.E.L.D. Jeffrey has said that he was a former superhero.
Jeffrey claims that he is an Inhuman, and possesses superhuman strength and invulnerability. He is capable of withstanding an impact from a barbell rod swung with human strength, displaying no significant reaction. And is capable of lifting an adult woman completely off her feet with one hand and slamming her into a wall hard enough to induce instant consciousness.
As the Director, Jeffrey displays human level skills with charisma and bureaucracy.
(In the comics Jeffrey Mace was The Patriot, a World War II hero with no superhuman powers. He briefly stood in for Captain America when he was in suspended animation until the modern day. He is also the uncle-by-marriage of General Ross, who also exists in Agents of S.H.I.E.L.D.)
