Database Replication Issue
You are asking for Master --> Relay --> Slave.  This is quite possible.


Server2: STOP SLAVE
Server2: Pretend it is a Master and do the operations necessary to add its first Slave (Server3).  (Dump data Server2, copy to Server3, etc)
Server2: START SLAVE


Be sure to turn on log_slave_updates and log_bin and have different server-id.

Why do you want M->R->S?  It is a rather unusual setup.  Is it the start of something more grandiose?  I ask because there may be other tips to impart.