As mentioned in
Properties of a direct connection to an ArcSDE geodatabase, no additional installation is needed on the client machine if you are going to make direct spatial database connections through ESRI products such as ArcGIS Desktop. However, the pg_hba.conf file does have to be altered to accept client connections. Consult the ArcSDE for PostgreSQL installation guide or the PostgreSQL documentation for information on altering the pg_hba.conf file.
The following steps are provided in case you need to create an OLEDB connection from ArcCatalog. Be sure the driver you install corresponds to the release of PostgreSQL to which you want to connect.