Exec the command using Agent Forwarding.

Allows a chain of ssh connections to forward key challenges back to the original agent, thus eliminating the need for using a password or public/private keys for these connections.

From the ssh(1) man page:

        Enables forwarding of the authentication agent connection.  This can also be specified on a per-host basis in a configuration file.

        Agent forwarding should be enabled with caution.  Users with the ability to bypass file permissions on the remote host (for the agent's UNIX-domain socket) can access the local agent through the forwarded connection.
        An attacker cannot obtain key material from the agent, however they can perform operations on the keys that enable them to authenticate using the identities loaded into the agent.