Transfer function of a frequency shifting system
The system you're looking for cannot be described by a transfer function because it is a time-varying system. Only linear time-invariant (LTI) system can be fully characterized by a transfer function. However, there is no LTI system that can shift frequencies. The output of a (stable) LTI system can only have frequency components that are already present in the input signal.

Frequency shifts are usually achieved by modulation, i.e., by multiplying the input signal with a sinusoid or with a complex exponential. Such a system is linear but not time-invariant.