It depends upon exactly what you need and how you want it to work. If you have something external monitoring things you could update the IP address and reload the configuration file. You can also use a dynamic DNS hostname and have that be updated, and then chan_sip will (based on your configuration) periodically do a DNS query and update itself.
If you are big enough, you obtain an autonomous system number and operate Border Gateway protocol, so that both interfaces are recognized, globally, as relating to the whole machine.