Will a 1998 suburban transmission fit 2003 Chevy Tahoe?

No, a 1998 Suburban transmission will likely not fit a 2003 Chevy Tahoe. While both are GM vehicles, there were significant changes in transmissions between those model years. The transmission type, bolt patterns, and even the computer control systems are different enough to make it incompatible. You'd need a transmission specifically for a 2003 Tahoe.