Linking Azure ExpressRoute to a different subscription
ExpressRoute in Azure consists of three components. An ExpressRoute Gateway, ExpressRoute Circuit and ExpressRoute Connection.
You cannot currently migrate any of these components to a different Azure subscription, you can, however, create a new ExpressRoute Gateway, within a new subscription, and link it to the existing ExpressRoute Circuit.
The steps involved are fairly straightforward. Delete the existing ExpressRoute Connection & Gateway, migrate any Virtual Machine or VNET resources to a new subscription and create a new ExpressRoute Gateway within the new subscription, then create a new connection from this gateway and you will see the option to choose the existing ExpressRoute Circuit.
Note: If you have created any VPN Gateways after your ExpressRoute connection they will most likely be dependant on the ExpressRoute Connection, therefore preventing you from deleting the connection until the VPN Gateway has also been removed. Removing the VPN Gateway will, unfortunately, lose the public IP address so your VPN may need to be reconfigured from your network side.