I guess it all depends on what does Design mean for the company you are working at.

Is design the product design? Is it the brand/marketing design?

Dirk pointed out most of the things a excellent Head of Design:

• Being able to define strategies and measure impact of these

• Promote design across the business and show the value design provides

• Understand the operational aspects of design and how to improve – reduce cost, encourage innovation

There are literary hundreds of things an excellent Head of design, it all depends on how mature the company/the team is.