This is a fact specific question that can’t be answered on the few facts you have provided.   It potentially implicates two areas of intellectual property law – copyright law and trade secret law.  Copyright law does not protect ideas – only expressions of those ideas fixed in a tangible medium.  If the concepts were reduced to a program (in software or written manuals) that expression would normally be protected by copyright.  While the executive director may take the position that she/he is the author for copyright purposes, if the executive director created the work as an employee within the scope of his or her employment, the charity would probably be the statutory author with the rights in and to the work under the “work for hire” doctrine.  

The program concept may also be a trade secret of the organization – something that gives it a competitive advantage and one that is protected against disclosure generally.  If so, taking the secret to another organization may violate the charity's rights to that trade secret. While the law generally protects a person’s knowledge capital – their knowledge and experience gained while working in one job – and allows it to be transferred to another employer, your situation may involve more than that, where the executive is taking a secret process or a copyrighted program and seeking to commercialize it at the new organization. 

If the former exec is just taking a concept that is publicly available and using it to replicate or improve the effort, the exec will probably be OK.  If the exec is using documents, computer programs, or some other kind of confidential information, there may be a problem.

(Thanks to Joseph T. Stapleton of Montgomery, McCracken for assistance in explaining these issues.)