The term 'Gulf States Bigwig' refers to a powerful leader in the Gulf States region. The two crossword solutions for this term are EMIR and AMIR, both of which are 4-letter words. An EMIR is an Arabic title of high rank or office, usually referring to a prince or ruler of a certain region. An AMIR is a similar title, but is used more commonly in Muslim countries. Both titles refer to a leader with a great deal of power and influence in the Gulf States region.