What you seek is called "zurcido".
Depending on your location, find a "costurera" and ask.
In my area there'd a Clothes Sanatorium (Sanatorio de la Ropa) on Juncal, between Talcahuano and Uruguay. Across the street from Josefina's bar and restaurant. First place where i'd ask.
Costureras and Sastres (tailors) have small shops here and there.
You can also try asking at your nearest laundromat.
Iz