Help identifying connector on vinyl shellhead
Often called an SME tonearm headshell connector 4-pin. 
The mating part is either a replacement SME 3009 or 3012 tonearm or a female SME tonearm 4-pin socket. Here are a few examples of available parts:

http://www.audiosilente.com/spare-parts-for-sme-new-sme-3009-connector-with-gold-plated-pins.html

https://www.ebay.com/itm/New-5pcs-lot-Technics-tonearm-headshell-SME-socket-connector-pure-silver-wire-/123834227569