Hello Angfe,
1) you should move one serial interface on the new router keeping the current IP addresses of the serial link.
On the LAN side: the current IP address on LAN interface of alreafy running C3800 has to become the VIP addres of the HSRP group, two additional IP addresses from the same IP subnet are needed on the LAN interfaces of the two routers both the ports have to be connected to the same broadcast domain.
You need also to configure tracking and preemption to make a complete HSRP configuration.
If eBGP is used on both serial links an iBGP session between the two C3800 routers is to be preferred.
2) the feature set must support BGP and HSRP. Using the same version of IOS image on both routers is a good idea
Hope to help
Giuseppe