The Imperial Diplomatic Corps (or IDC) reports to the Senate. Officially it operates embassies in most foreign systems, but the IDC has far-reaching powers too and unlike other police units has jurisdiction throughout the Empire. It can support Senators and Ambassadors abroad.
The Ambassadors are the visible members of the IDC; high-ranking Imperial officials usually reporting directly to a specific Senator with an interest in their area, but also reporting directly to the Senate. Each Ambassador has a significant staff and budget to project Imperial influence. This staff is said to include secret agents that operate covertly within foreign powers and corporations, but reporting back ultimately to the Ambassadors, then on to the Senate.