Well, I see a couple of possibilities.
1: Charles V conquers East-Frisia, just like he conquered Frisia, Gelre, etc.
2: The Dutch Republic (or maybe the house of Orange-Nassau or the province of Groningen or Friesland) annexes it after the death of the ruling line (like Prussia did). It has happened with a lordship like Vianen, it might have happened with East-Frisia
3: the Dutch republic simply conquers it somehow (unlikely though as the Dutch republic wasn't expansionist)
4: the kingdom of Holland survives somehow
5: The United Kingdom of the Netherlands gains East-Frisia after the Napoleonic Wars (maybe as compensation for the loss of Luxemburg?)
6: The Netherlands is occupied by Germany during WWI and gets East-Frisia as compensation (like the Belgians got Eupen-Malmedy)
7: After WWI the allies give Belgium Dutch Limburg and Zeelandic Flanders (as the Belgians demanded) and the Netherlands get compensated with East-Frisia
8: The Netherlands is occupied by Germany during WWII and get East-Frisia after the war as compensation (Bakker-Schut, but smaller)