Hi,
The easier way to do this is to add the new switch to one of the existing vlan/subnet if you have enough IPs. This way you don't have to worry about a new vlan, new subnet, and firewall configuration.
Question: are you connecting this new switch to another switch or directly to the firewall. If it is to another switch, you can just configure a trunk port between one of the existing switches and the new one and use an existing vlan and if directly to the firewall, you should be able to do the same as long as the firewall supports layer-2.
HTH