baton

pass (or hand) on the baton hand over a particular duty or responsibility.

☞ In athletics, the baton is the short stick or rod passed from one runner to the next in a relay race. The related phrases pick up or take up the baton mean 'accept a duty or responsibility'. Compare with hand on the torch (attorch).

under the baton of (of an orchestra or choir) conducted by.

☞ The baton here is the rod used by the conductor.