CEIC = CREC ?

If we're okay with:

COMITÉ ETICO DE INVESTIGACIÓN CLÍNICA = CLINICAL RESEARCH ETHICS COMMITTEE

then it follows that the acronyms would be

CEIC = CREC

But, unless their is an English equivalent (EG NATO for OTAN), I think the style rules say we should use the source abbreviation....

Quoting:
If an abbreviation/acronym that does not have an official English version appears:
– In the body of the text:
Use the abbreviation/acronym followed by the full source in italics and between parentheses, and then provide the translation between hard brackets. E.g., “UWG (Unlauterer Wettbewerbsgesetz [Unfair Competition Act])”. Use only the abbreviation/acronym thereafter.

Okay,

so it would be

CEIC (Comité Etico de Investigación Clínica [Clinical Research Ethics Committee])   ... for the first mention.

And every subsequent mention would be simply CEIC, as per the guide:

Language Guide wrote:Use only the abbreviation/acronym thereafter.

Yes, with source language in italics