Stories of gods having to fight other gods for dominance over the world are quite common in mythology, but there are a few different sorts. Some have the new gods overthrowing older, established ones. Others have gods going to war after they’ve already been established, or conquering threats to their rule. I’ve seen a few mentions of the karuilies siunes, or former gods of Hittite mythology. Like the Greek Titans, they’re said to have been conquered by the current gods and imprisoned in the Underworld. Hurrian and Hittite mythology tell of the primordial god Alalu being overthrown by his cupbearer Anu, then another god named Kumarbi castrating Anu and swallowing his genitals, which somehow leads to the storm god Teshub being conceived inside his body.
After Teshub is removed, Kumarbi tries to eat him, but ends up eating a rock instead. Teshub isn’t his only oddly born son, either. At one point, on the advice of a sea deity, he has sex with a boulder, which then gives birth to an enormous stone giant named Ullikummi, who is bound to the shoulders of another primordial god who supports the sky. There’s a long conflict between Kumarbi and Teshub, the former allied with earth and sea gods and the latter with ones from the sky. The former gods are said to usually be allies of Kumarbi, but they help out Teshub in one case. Due to gaps in the cuneiform records, we don’t actually know what happened to Kumarbi. There are a lot of similarities between him and Kronos: they castrated their predecessor and then tried to devour their offspring, only to be tricked and eventually overthrown. Kumarbi himself does not appear to be one of the imprisoned elder gods, however. These old gods have also been identified with the Babylonian Anunnaki, also often said to live in the Underworld, and people would sometimes try to gain their assistance through sacrifices made in pits.
The Babylonians also had the myth of Marduk overthrowing Tiamat and then making the world from her body, much as Odin and his brothers did with the corpse of the giant Ymir.
There’s a similar story told of the primordial figure Pangu in Chinese mythology.
And in Celtic mythology, the Tuatha De Danann took over Ireland from the monstrous Fomorians, most of whom were then driven into the sea.
In most of these cases, the older gods are chaotic beings who are often more forces of nature than the more humanoid ones who were actively worshipped, so there’s a sense of progress. This isn’t always that clear cut, however, as Kronos is said to have ruled during the Golden Age of humanity. He was a horrible father, but I don’t know that he was necessarily supposed to have been a bad ruler. And there are gods in the Greek pantheon who were identified as Titans, but were worshipped alongside the Olympians, and were allies of theirs after the Titanomachy. So it might not even be so much that the current gods are improvements as it is a recurring theme that they had to fight for their positions.
This fighting doesn’t always end once the gods are enthroned, either. Both Zeus’s battle with Typhon and the invasion of the Gigantes happen after he’s already become king.
The war between the Norse Aesir and Vanir is said in the Poetic Edda to be “the first in the world,” yet it’s presumably after the creation of the worlds.
There’s also no clear winner, instead ending in a truce and hostage exchange. The Aesir seem to be in a similar stalemate with the Jotuns, the two sides never friendly and sometimes outright fighting each other, but other times they’re on at least somewhat friendly terms, and some of the gods take giants as spouses or lovers. This fits a general difference in tone between Greek and Norse mythology. Zeus constantly proves that he’s more powerful than any challengers, while Odin and company can only achieve temporary victories, and they and their enemies are mostly doomed to die at Ragnarok. In Hindu mythology, the Devas and Asuras are said to be in constant conflict.
While I suppose the gods were often thought to be eternal, I have come across cases of their having chosen successors in the future. The general summary of Ragnarok has it that, after the world is destroyed and reformed, Baldur and his brother Hodur would come back to life to rule the world with the help of Thor‘s sons Magni and Modi.
The Chinese Jade Emperor‘s intended successor is Kin-k’ue Yu-chen T’ien-tsun, the Heavenly Master of the Dawn of Jade of the Golden Door, just as he himself was the hand-picked successor to Yuanshi Tianzun, the Primeval Lord of Heaven. Even the Greeks seem to have had some concept of a potential heir to Zeus, who was given the name Zagreus. I came across a brief reference to the name in a book years ago, but more recently it’s come up as that of the protagonist of the video game Hades. I know pretty much nothing about the game, but it makes him the son of Hades, while the Orphic Mysteries claimed that he was the son of Zeus and his own daughter Persephone.
The basic story is that Hera convinced the Titans to tear Zagreus apart, but Zeus saved his heart and made it into a potion that he gave to Semele, who then gave birth to Dionysus.
I haven’t seen any indication that the reborn Dionysus is Zeus’s chosen heir, however; I guess he gave up on that idea. That said, Aeschylus seems to have regarded Zagreus as the son of Hades, so that wasn’t just made up for the game. We do know that Zeus, for all the kids he had, fell into his father’s habits when faced with the prospect of being overthrown by his own child. He swallowed his wife Metis, who then gave birth to Athena, born out of his head. It appears that the earlier version of the myth is that Zeus produced her without a woman being involved, with her emerging from his head fitting her role as the personification of wisdom. Regardless, Athena has no intention of overthrowing her father.