The Greek for this verse is literally “For God will show to every under heaven your splendor.” Whether a word has dropped out of the text or not, “every under heaven” clearly means “every nation on earth” (Good News Translation). An alternative way to express this verse is “because God will let every nation on earth see your brightness [or, splendor].” The connector For expresses a logical relationship with the previous verse, so it should be translated.

Quoted with permission from Bullard, Roger A. and Hatton, Howard A. A Handbook on The Shorter Books of the Deuterocanon. (UBS Helps for Translators). New York: UBS, 2006. For this and other handbooks for translators see here.