Relationships will improve on a diplomatic level no doubt. The players in the region are using their cards against Turkey, and so it will be forced to reconcile with Israel sooner or later. The Israeli's have already expressed their willingness to work together with Turkey if i'm not mistaken.
@500 @Archdemon @DavidSling
Israel and turkey will both profit from improving the relations between them.
Israel side
Israel will earn a strong and close (geographical) ally in a troubled region.
Israel will export it's gas to turkey and probably to other countries in europe.
Israel and Turkey will cooperate on regional issues and on other economic,industry(mostly military) matters.
Israel will earn more political power thro gas deals.
Turkey side
Turkey and Israel got common ground on many middle eastern issues.
Turkey will retain it's position as gas provider to the rest of the EU.
Turkey will be able to benefit from Israel's experience in modern warfare and technology like before.
Turkey will gain a strong regional ally in a troubled time.
United States
Two of it's close allies will cooperate together
Nato and EU
Two of it's close allies will cooperate together
Besides, improving relations with Israel will help Turkey improve relations with Egypt, which is another strong and stable ally in the ME