A statutory body tagja, azaz a board of directors tagja ez a statutory executive - az executive itt felsővezetőt jelent (nincs köze végrehajtáshoz /execution/), akit döntési ill. képviseleti joggal ruháztak fel (has jurisdiction over ....)
Szövegkörnyezetet jó lenne látni... Szerintem nézd meg, hogy a forrásszövegben szereplő konkrét cég milyen vállalati formában működik és ennek megfelelően kiválasztani a legjobb magyar megfelelőt. Néhány példa segítségül:

Statutory Bodies of the Company
Board of Directors
The Board of Directors performs a pivotal role within the corporate organization. Its tasks and responsibilities include setting strategic and organizational guidelines, ensuring adequate controls to monitor the performance of the Diasorin group.
The Board of Directors has jurisdiction (which may not be delegated to anyone) over the adoption of resolutions concerning the following: ...
http://www.diasorin.com/en/company/corporate-governance/stat...

Due to the ambiguous legal regulations, the Czech courts had to often evaluate the question whether a member of a statutory body (an executive or a member of the board of directors) of one company, can be also employed by the same company for e.g. in a position of a managing, executive or financial director.
http://legalknowledgeportal.com/2012/03/06/parallel-executio...