This answer is not for grading, but only:

1. to demonstrate to the asker how most seemingly difficult translation issues can be resolved with a bit of self-conducted research; and

2. to demonstrate to answerers that providing an opinion abou what the term means does not help the asker. The asker needs a reliable reference.

I have googled the expression "consular access," and the first item was the following:

http://travel.state.gov/law/consular/consular_747.html

"Arrests and Detentions of Foreign Nationals

Whenever a foreign national is arrested or detained in the United States, there are legal requirements to ensure that the foreign national's government can offer him/her appropriate consular assistance. In all cases, the foreign national must be told of the right of consular notification and access . In most cases, the foreign national then has the option to decide whether to have consular representatives notified of the arrest or detention. In other cases, however, the foreign national's consular officials must be notified of an arrest and/or detention regardless of the foreign national's wishes. Whenever a foreign national is taken into custody, the detaining official should determine whether consular notification is at the option of the foreign national or whether it is mandatory . A list of all embassies and consulates in the United States, with their telephone and facsimile numbers, is included in this booklet to facilitate the provision of notification by detaining officials to consular officials when required."

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Note added at 1 hr 42 mins (2005-03-13 23:11:34 GMT)
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http://ara.amnesty.org/library/Index/ARAAMR511012000?open&of...

In case the detainee is a foreign national, he should have access
( communucation)with the embassy or consualate of his country

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Note added at 5 hrs 44 mins (2005-03-14 03:13:48 GMT)
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http://www.unis.unvienna.org/unis/pressrels/2001/sgsm7917.ht...
The Secretary-General remains concerned at the continued detention of eight international and 16 national staff of Shelter Now International by the Taliban. He regrets that, contrary to customary international law, consular access and legal representation for the detainees have been denied. AS WE CAN SEE LEGAL REPRESENTATION WAS ALSO MENTIONED.

المعني المشار إليه أعلاه يجيب على أنه ليس لهذا الطرف الحق في طلب التدخل القنصلي
والله أعلم