To become experienced in worldly ways and social maneuvering; to become sophisticated or worldly-wise — often with a slightly critical nuance.
都会で働くうちに彼はすっかり世慣れてしまった。
While working in the city he became completely worldly-wise.
幼いころから商売に携わった彼女は世慣れた口調で話す。
Having been involved in business since childhood, she speaks in a worldly tone.
世慣れた態度は時に冷たく見えることもある。
A worldly manner can sometimes seem cold.