What will be happen to live and existing connections when failover HA BIG IP active-standby

Zen_Y 
MAC masquerade will use gratuitous ARP. As a first step, you should ensure that your network switches can handle gratuitous ARP. If gratuitous ARP is disabled on your network, you may experience at least 5 minutes of outage.
As others have said, for "existing connections", Connection Mirroring is the solution.