As of now, there's no official answer, but at least older than 4200 years.
Summarizing from the Wikia about Fairy Clan:
Longevity: The average lifespan of a Fairy is between 1000 to 1500 years. They do not appear to physically age and they never suffer from illness.
Now, comparing the known fairies' age:
- Invisible: ?
- Cisca: ?
- Dahlia: ? (former, 2nd king/queen)
- Melik: ?
- Elaine: ±1000
- Ende: 1000+
- Puora: 1000+
- Helbram: ±1300 (deceased)
- King: 1300+ (current king)
- Gloxinia: ±1400 (former, 1st king)
- Gerheade: ±4200
Although most of them are mentioned in between 1000-1500 range, Gerheade is an exception, and she's not even a king.
Thus, assuming there's nothing that prevents their natural aging (e.g. Elaine, Helbram), and since they don't suffer any illness, fairy king should even be possible to live more than 5000 years.