expression, ichidan verb
take up residence; settle down
A somewhat formal or literary expression for establishing one's home in a place.
彼は京都に居を構えて、執筆活動に専念した。
He took up residence in Kyoto and devoted himself to writing.
住む is the common, everyday verb for 'to live (in a place)'. 居を構える is more formal and emphasizes the act of establishing a residence.
Compound of 居 (residence) + を + 構える (to set up, to establish). The phrase literally means 'to set up a residence'.