A GPO was setup with filtering applied to a single group containing computer objects. Is a restart mandatory for all the computer objects listed in the "New Group" for GPO to be applied on them? or is there other way without restart?
Do you mean that you just added the computer accounts to the Security Group you're using in your GPO filter? If so, then the computers need to be rebooted.
No, while there are ways to get a new Kerberos token with refreshed group membership, a reboot is required for everything to take effect.