No, the acronym ‘REX’ has nothing to do with BREXIT. It’s not even a distant cousin. The term ‘REX’ has only one thing in common with BREXIT. Both have something to do with the EU (European Union). REX is about exporters, the EU, GSP, certificate of origin et al.
‘REX’, in fact, stands for 'Registered Exporter (REX)'. The 'REX system' is a “system of certification of origin of goods that will be applied in the Generalised System of Preference (GSP) of the European Union as from 1 January 2017. It is based on a principle of self-certification by economic operators (read ‘exporters’) who will make out themselves so-called statements on origin. To be entitled to make out a statement on origin, an economic operator will have to be registered in a database by his competent (customs) authorities. The economic operator will (then) become a "registered exporter".”
To effectively apply the REX system, a GSP beneficiary country has to satisfy two specific prerequisites as defined in the Regulations. Although about 38 countries have agreed to adopt the system with effect from 1 January 2017, it appears that only India, Kenya, Laos, Nepal and Zambiahave fulfilled the two necessary criteria.
In the REX system, the following types of traders/exporters will be registered:
Exporters in GSP beneficiary countries
European Union operators exporting to GSP beneficiary countries for the purpose of bilateral cumulation of origin
European Union operators exporting to third countries with which the EU has an FTA where the REX system is applied
European Union operators replacing proofs of origin initially made out in GSP beneficiary countries
How does it work? It's very simple, really. Briefly stated, the stages are as follows:
To become a registered exporter, an exporter shall lodge an application with the competent authorities of the beneficiary country where he has his headquarters or where he is permanently established. (Article 86.1 of Regulation 2015/2447)
Authorities check whether application is complete
Authorities accept application and register exporter in the system
European Commission receives information on registration of exporter and maintains central database of registered exporters
Information about exporter (except the 'confidential' data) is published on the internet.
The rules, regulations and the detailed procedures are available in the EU document titled “COMMISSION IMPLEMENTING REGULATION (EU) 2015/2447 of 24 November 2015 - Laying down detailed rules for implementing certain provisions of Regulation (EU) No 952/2013 of the European Parliament and of the Council laying down the Union Customs Code.” This document can be found at: http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32015R2447
The document on the ‘Regulations’ is very comprehensive, addressing both regulatory and procedural aspects. At the same time, it is far too extensive and detailed for ready comprehension. It may be advisable, therefore, to access other documents released by the Commission that provide snapshots and guidance on what ‘REX' is all about and the procedures to follow. A document titled, “The Registered Exporter system (the REX system)”  could be a very good starting point.
This brief introduction is to sensitise those who are yet to get acquainted with ‘REX’, especially the exporters, including everyone dealing with the export of goods from the affected countries.