Virtual LANs are logically separate much as would be physical LAN segments. So if you place workstations within one VLAN and servers in another they would be unable to see each other unless you bridge or route between them. For the former, they could retain the same addressing, but it negates the usual purpose for making separate VLANs. For the latter, you would need separate subnets. If your servers were hard address coded, using low addresses in the /24, and the workstations were using DHCP, you might be able to split the /24 into two /25s leaving the server addresses alone, although their gateway address and gateway mask might need revision. (Of course if workstations were DHCP addressed, it might be easier to migrate them to a new /24.)

PS:

What someone might want is stop using VLAN 1 for servers (and workstations?). VLAN 1 often has some default managment traffic that rides on it. So, it's often a good idea to place normal hosts into a different VLAN. Host addressing for the new VLAN probably could be left exactly as used now for VLAN 1.