The call sign Clipper came into use when Pan American started flying boat services to South America in 1931. The flights would call up using the aircraft's Clipper name. This was continued on both the Pacific and Atlantic throughout the 1930s.
Post war the aircraft started to use Clipper plus registrations without the NC or later N prefix.
I had access to an HF radio in the late 1950s. Pan American piston engined flights would generally call up as Clipper followed by the last three of the reg. When the 707 started on the Caribbean and the Atlantic, the flights used Jet Clipper plus the last three of the reg. Flight numbers came into radio callsigns around 1962/3