This is the 11357th most frequent Spanish word.
establecerse
To settle or establish oneself.
The verb 'establecerse' here means 'to settle' or 'to establish oneself', referring to the act of moving and adapting to a new place of residence.
La familia decidió establecerse en una nueva ciudad para buscar mejores oportunidades.
The family decided to settle in a new city to seek better opportunities.
In this sentence, 'establecerse' is used to express the action of settling in terms of choosing a permanent place of residence after a period of being transient.
Después de años viajando por el mundo, decidió establecerse en su país de origen.
After years of traveling the world, he decided to settle in his home country.
Here, 'establecerse' means 'to establish oneself', but in the metaphorical sense of aiming for prominence or recognition in a specific domain.