The 28-year-old moved to the Ashton Gate club on an initial three-month loan deal in October.
"Central midfield is where we feel we are a little light and actually somewhere we'd like to strengthen," City manager Steve Cotterill told the club's official website.
"Simon's a great professional and a tidy, intelligent footballer. He reads and understands the game well."
Gillett has made 10 appearances for the League One outfit this season.