Is conspiracy of subornation of perjury committed by the first party if the second party never agrees nor gives false testimony?

No, conspiracy to commit subornation of perjury would not be established if the second party never agrees to commit perjury or provides false testimony. For such a conspiracy to exist, there must be an agreement between the parties to engage in the act of encouraging or persuading someone to provide false testimony. Without that agreement or any false testimony occurring, the elements of the crime are not met.