When Helbram's history is revealed, I realized that Harlequin as the Fairy King and his sister Elaine should have wings. How come they don't have wings?
Recently picked up NNT and had a similar query immediately when King's old friend was revealed. Searching around I've found that no concrete reason for the "Wingless King" of the Fairies.
However there are a couple theories around with some supporting evidence.
King's Wings have not yet matured
Though King may be quite old, it seems that he can't yet spread his wings. The age old cocoon to butterfly theory.
King's wings growing may also allow him to "level-up" to fight the 10 Commandments on an equal footing. This is shown in Chapter 134 of the manga, when King and Meliodas square off Meliodas counters King's spell. While it did nothing immediately, we see that King's back gets hurt and he has a dark spot. Maybe the spell weakened something that was holding back the growth of King's wings?
King and Elaine are not full fairies
Since only the siblings are the only fairies shown without the wings, we can assume that it may be due to their ancestry? Maybe he is just half-fairy. Apart from this there is no evidence for what mix they have.
Given that the wingless nature of King has been addressed in the manga (Chapter 134.10), we can assume this is a part of some reveal that the mangaka has planned and will be shown in the future releases.