Wiktionary
vb. (context idiomatic English) Be pre-eminent; have the greatest influence (over someone or something); dominate.
WordNet
v. be master; reign or rule
Usage examples of "hold sway".
The Directors of the Office of Cultural Amity hold sway over who will be named Sovereign for life.
If you are working in a group that includes someone with a mathematical bent, they can calculate and note here the times of the day at which particular planets and angels hold sway (see the tables on pages 235 and 239 for methods of calculation).
Even the great prophet Zoroaster did not deny it would hold sway on this earth.
I repeat: in Turgosheim the Lords, and of course the Ladies, hold sway.
Since it seems I now hold sway, I hereby testify to your ascension .
The Uniformitarians hold sway, when it comes to the granting of tenures and honors.
She might have had difficulty with the notion that Worf was prepared to sacrifice her rather than allow dishonor and dereliction of duty to hold sway.