The option to publish services to a stand-alone ArcGIS Server site is only available in ArcGIS Pro 2.3 or later, and the publishing steps vary between the versions. The ArcGIS Server site must be deployed on ArcGIS Server 10.6 or later to enable publishing services to the stand-alone site. ArcGIS Server 10.5 and earlier versions do not support this feature.
ArcGIS Pro 2.4
Publish the map service directly to a connected stand-alone ArcGIS Server. A publisher or administrator server connection is required for publishing privileges to the stand-alone ArcGIS Server site. Refer to ArcGIS Pro: Publish a map service for steps to do this.
ArcGIS Pro 2.3
Publish the map service with the arcpy.sharing module by creating a sharing draft for ArcGIS Server using the arcpy.sharing CreateSharingDraft function. Refer to ArcGIS Pro: MapServiceDraft for steps to do this.
ArcGIS Pro 2.2
ArcGIS Pro 2.2 and earlier versions do not support this feature.