Technically The Second Republic of Morrowind, following the dissolution of the Hlaalu kingship and exit from the Empire in the early Fourth Era, it is still referred to as simply "Morrowind."
With the dissolution of the kingship and destruction of the Tribunal, Morrowind was briefly subject to the Nerevarine as Hortator. However, he vanished in the early Fourth Era, leaving the Grand Council as the absolute power. Before his disappearance, the Nerevarine successfully lead House Redoran's rebuilding projects, culminating in the Pillar of Accession--commemorating the Argonian's expulsion from Morrowind and recovery from the Red Year.
Following these events, House Redoran was the military, economic, and political juggernaut of Morrowind. In 4E 40, the Nerevarine vanished, giving up his virtual kingship of Morrowind, never to return.
House Redoran enacted several policies to take Morrowind along a new path, free of the Empire and of the monarchy. All Imperial titles or those not connected to a Great House--i.e. Dukes, Counts, Kings--were declared defunct. Those who had been House Hlaalu were simply stripped of their lands, titles, and wealth without compensation. Non-Hlaalu who possessed Imperial titles were given either a respectable position in their House or wealth in exchange for the loss. Out of this reformation, Morrowind gained two new Great Houses: Indaram and Uvenim.
By 4E 50, most of Vvardenfell had been rebuilt, the Argonians had been pushed out of Morrowind, and the seven Great Houses of the Grand Council were regularly convening in their new capital: Blacklight.
Morrowind has a state religion, "the Temple of the Reclamations," often referred to as just the New Temple. It is centered around worship of Azura, Boethia, and Melphala, with Azura as the chief diety. It holds many saints in its canon, the most venerated of them being Ulain Nerevarine and Indoril Nerevar.