Nothing happened to him.
He was not replaced by another sea deity because he was the Sea itself: the Mediterranean and Black Seas in particular were supposed to be his body, in the same way that the Earth was the body of the goddess Gaia, the Sky was the body of Ouranos [Uranus], and the Underworld Abyss was the body of Tartaros [Tartarus].
When the Olympians took over the rule of the cosmos, Pontos [Pontus], being simply a part of the structure of that cosmos, continued to exist therein, similarly to how Aither [Aether] was a portion of the upper region of said structure and Erebos [Erebus] was part of the lower segment thereof.
The more prominent sea deities, along with all other marine life, dwelt within the body of Pontos, just as all land creatures lived on Gaia's surface, while certain Underworld inhabitants, including the vanquished Titans, were housed within the body of Tartaros.
Pontos is very similar to certain of his fellow primordial deities, Erebos and Tartaros especially, in that his only functions in the mythology are to serve as an essentially inert part of the makeup of the universe, and to become the parent and ancestor of other gods who go on to become important figures in both myth and cult. Beyond these roles, there is only once instance of ancient literature in which Pontos is characterised at all, namely in Philostratus the Elder's Images.
The scene occurs many thousands of years after the end of the Titans' War, during the expedition of the Argonauts, one of whom was Orpheus, whose music was so powerfully beautiful that rivers changes their courses to follow him and wild animals were temporarily tamed, herding with domestic ones in order to listen to him play. In Images 2.15, while the Argo is passing in between the Clashing Rocks at the Bosporus, Pontos hears Orpheus' music and is calmed "under the spell of his song."
A couple of descriptions in Aeschylus' play Prometheus Bound come close but fall just short of actual characterisation. In Lines 89-90 of the play, the Titan Prometheus refers to "the numberless laughs of the waves of Pontos" (pontíon te kymáton anḗrithmon gélasma). Wiktionary interprets these "laughs" or "smiles" as signifying the waves of the Sea "sparkling in sunlight." In Lines 431-432: "The waves of Pontos utter a cry as they fall," and "the Deep [Bythós] laments" the pain of the imprisoned Prometheus.
Most of the five children of Pontos as listed in Hesiod's Theogony and Apollodorus' Library are background characters on the same level as their father, essentially the elderly part of the community of marine divinities, whose only purpose in the myths is to be ancestral figures. Nereus and, to a much lesser extent, Phorkys [Phorcys] are the exceptions. Otherwise the only thing that Keto [Ceto], Thaumas and Eurybia are known for is being the progenitors of monsters, gods and Titans who became way more important than they.
I haven't found any mention of there having been a cult of Pontos anywhere. He does feature in some late mosaic artwork from Roman Africa as the personification of the surface of the sea, with ships resting upon his body and such. Thalassa, a female personification of the Mediterranean Sea, was way more prominent than he, being mentioned much more often, which perhaps, from what I can tell, is because thalassa (and similar forms of this word) is the primary term in Ancient Greek when referring to the sea. (According to Hyginus the first fishes were the offspring of Pontos and Thalassa.)