Fetching details from the dictionary...

to join (cloth, wood, etc.)
「接ぐ」 has another reading with different meanings.
二枚の布を丁寧に接いで一枚に仕立てた。
I made it by joining two pieces of cloth.
職人が二枚の板を丁寧に接いだ。
The craftsman carefully joined the two boards together.
古い着物の布を接いでいる。
She is joining pieces of old kimono fabric together.