Fifth king of Rome but Etruscan by birth. Made king over the claims of the living heirs of Ancus Marcius, fourth Roman king. The histories say Ancus Marcius himself chose Priscus as his successor but something doesn't seem right in this account. It was not unheard of for a people to chose a king from another city, empire, realm - among other things it could prevent rival factions backing rival candidates from plunging a kingdom into civil war. But the Romans? Arch-belligerents and warlike as they were accepting a foreign king when living heirs were available?
We know, from evidence like pottery sherds and burial rituals, Rome went from being a Latin city to an Etruscan one early in its history. We know the Latins had no exceptional skill as engineers while the Etruscans were famed as engineers and city-builders. In particular, the Etruscans were the spectacular with sewers and irrigation.
The cloaca maxima (great drain) was begun during the reign of LTP.
What happened was not a conquest, at least not in the sense the Romans used the term. Rome did not suffer a military defeat. Nor was there a treaty by which Rome left Latium and joined Etruria. It is not even sufficient to consider this a case of an "advanced" culture displacing a "primitive" one. Plutarch and Livy both write the Tarquinii chose to come to Rome and the Romans chose to make them kings. Michel Serres tells us legends in history serves the same purpose as legends on maps - they tell us how to read what is there to be read.
So the Tarquinii came to Rome and Rome captured them. It is the precise analog to Rome's military conquests but with a geographical variation. Rome rarely destroyed what it conquered. Anything that came within Rome's grasp became part of Rome, eventually becoming Roman.
Etruscan influence in Roman culture can be seen in many areas but I want to focus on one; Latin gods were not anthropomorphic. Ogilvie tells us Latin religions were aniconic. Prior to the influence of Etruscan culture, religious practice in Rome centered on the altar - a fixed location where sacrifices were offered. The idea of divinities who could be visualized, who existed in space themselves, was Etruscan (probably by way of Greece, with whom the Etruscans traded).
The Etruscan influence in Rome created a kind of expansion in religious architecture. Originally, worship was conducted around a single point, the altar. When the altar was (partially) replaced by Etruscan temple architecture, the point was expanded to a precinct - the templum. Despite the similarities between templum and the English 'temple', the templum does not refer to the building but the sacred area in which the building is located. It is a point expanded. No difference existed between the center of the templum and the edge.