Disclaimer
The Author of this posting offers the information contained within this posting without consideration and with the reader's understanding that there's no implied or expressed suitability or fitness for any purpose. Information provided is for informational purposes only and should not be construed as rendering professional advice of any kind. Usage of this posting's information is solely at reader's own risk.
Liability Disclaimer
In no event shall Author be liable for any damages whatsoever (including, without limitation, damages for loss of use, data or profit) arising out of the use or inability to use the posting's information even if Author has been advised of the possibility of such damage.
Posting
Should be no need to reboot routers. I would, though, be concerned about changing the virtual gateway IP, for the same group, while any HSRP group peers are active. What John suggested might work fine, but I would recommend taking down the standby group peer(s), then changing the IP for the hot HSRP peer, then reactivating the standby group peer(s) (also with the new IP). Functionally, this should be like changing the interface's "real" IP.
Another method, if your devices support mHSRP and you're not committed to using a particular group number, define the new IP under a new standby group. This can ease the transition of hosts from old to new IP as both will work. Once the transition is completed, remove the original standby group.
