CLEAR Act of 2013

Clear Law Enforcement for Criminal Alien Removal Act of 2013 or the CLEAR Act of 2013 - States that: (1) state and local law enforcement personnel, in the course of their routine duties, have the inherent authority to investigate, apprehend, or transfer to federal custody aliens in the United States (including interstate transportation of such aliens to detention centers) in order to assist in the enforcement of U.S. immigration laws; and (2) effective two years after enactment of this Act, a state that has in effect a statute, policy, or practice prohibiting such law enforcement assistance shall not receive certain federal incarceration assistance.

Provides for the listing of immigration violators in the National Crime Information Center database.

Directs states and localities to provide the Secretary of Homeland Security (DHS) with specified information about apprehended aliens who are believed to be in violation of U.S. immigration laws. Provides federal reimbursement for related state and local costs. (States that such provision shall not require state or local enforcement officials to provide DHS with information related to a victim of a crime or witness to a criminal offense.)

Directs the Secretary to make grants to states and political subdivisions that enforce immigration laws in the course of their routine law enforcement duties for special equipment and facilities related to arresting, detaining, or transporting illegal aliens.

Directs the Secretary to: (1) construct or acquire 20 additional detention facilities for aliens detained pending removal (or a decision on removal); and (2) consider the transfer of military installations under base closure laws for such purposes.

Amends the Immigration and Nationality Act regarding illegal aliens apprehended by state or local authorities to provide for: (1) federal custody upon state or local request; and (2) state or local compensation for related incarceration and transportation costs.

Directs the Attorney General (DOJ) or the Secretary to ensure that the detention of an alien subject to removal is in an adequate state or local prison, detention center, or other comparable facility prior to his or her removal examination.

Directs the Secretary to establish immigration-related training for state and local personnel.

Provides: (1) personal liability immunity to the same extent as corresponding federal immunity for state or local personnel enforcing immigration laws within the scope of their duties under this Act; and (2) civil rights money damage immunity for state or local agencies enforcing immigration laws unless their personnel violated criminal law in such enforcement.

Continues the institutional removal program (IRP), which shall be expanded to all states.

Authorizes state or local detention of an illegal alien after completion of such alien's prison sentence for: (1) up to 14 days to facilitate federal transfer; or (2) until transfer to the U.S. Immigration and Customs Enforcement.

Authorizes appropriations for FY2014 and subsequent fiscal years for the state criminal alien assistance program (SCAAP).