In the relation between a client & supervision consultant, what FIDIC contract shall follow? The design shall be checked by an engineer in the red book.

In the relation between a client & supervision consultant, you should follow FIDIC form of the Client/Consultant Model Services Agreement 4th Ed (2006 White Book).

This is applicable for both RED Book and Silver Book wherein under RED Book, Consultant have greater responsibility of design whilst under Silver Book its responsibility is minimum except for defining Employer’s Requirements and Performance Criteria definitions.