Will a 2003 saxo vtr gearbox fit 1997 vtr?

No, the gearboxes are not compatible. The 2003 Saxo VTR has a six-speed gearbox, while the 1997 Saxo VTR has a five-speed gearbox. The bellhousings are also different, so the 2003 gearbox will not bolt up to the 1997 engine.