U won't get a U.S. CPL-IR with your JAR CPL-IR, but U may apply for a U.S. PPL-IR. Here's what FAR Part 61, Subpart B, Sec. 61.75 says (abridged version) :
(a) A person who holds a current foreign pilot license issued by an ICAO State may apply for and be issued a PRIVATE pilot certificate with the appropriate ratings.
(b) Such a U.S. private pilot certificate shall specify the person's foreign license number and country of issuance.
(c) Aircraft ratings listed on a person's foreign pilot license may be placed on that person's U.S. pilot certificate.
(d) A person who holds an IR on the foreign pilot license may be issued an IR on a U.S. private pilot certificate provided:
(1) The person's foreign pilot license authorizes instrument privileges;
(2) Within 24 months preceding the month in which the person applies for the instrument rating, the person passes THE APPROPRIATE KNOWLEDGE TEST
(e) A person who receives a U.S. private pilot certificate that has been issued under the provisions of this section may act as a pilot of a civil aircraft of U.S. registry in accordance with the private pilot privileges authorized by this part
(f) Only one foreign pilot license may be used as a basis for issuing a U.S. private pilot certificate.
(g) A U.S. private pilot certificate issued under this section is valid only when the holder has the foreign pilot license upon which the issuance of the U.S. private pilot certificate was based in the holder's personal possession or readily accessible in the aircraft.
MF