When should your staffing agency realistically give you confirmation of a contract extension or renewal?

Hello Reddit! I have been employed as temporary worker for the City of Houston in the public health department through 08/21/20-12/30/20.

All my coworkers refer to me as integral part of the job site ( Since not only I’m a temperature screener, I’m also a runner) And all superiors like me, So my question is with the contact nearing it’s end. When should a staffing agency reach out to you for a extension? Should I job search? Should I stay on or should I jump onto some other employer?

Thank you in advance!