With the collapse of the original incarnation of S.H.I.E.L.D., some members who were opposed to Hydra saw an opportunity to move away from Director Fury's 'cloak and dagger' remit and instil more transparency and accountability. These people did not rejoin Coulson's new "official" version, but instead struck out on their own, keeping their very existence a secret.
Unlike the original S.H.I.E.L.D. that had one director with authority over all other agents, this version of S.H.I.E.L.D. had a more democratic style leadership with a board of directors that reached decisions based on majority rule.
During the events of Avengers: Age of Ultron it was revealed that the mysterious "theta protocol" was a secret helicarrier Fury and Coulson had built and used to save thousands of lives. With Coulson's greatest secret revealed, Gonzales felt Coulson could be trusted again and thus the two S.H.I.E.L.D.'s united as one organization.