In Fate series, what would happen if a master won the Holy Grail War but did not have any wish for the Holy Grail and did not destroy it? What would happen then?
Quite simply the Servant will demand their wish to be granted
Although too powerful to be controlled by humans, they are bound by three Command Spells, representing the Masters' "right to rule" over them, with obedience towards the Command Spells being the "absolute condition required for materialization." Due to the prospect of having a wish granted by the Holy Grail, it also serves as an incentive to cooperate with the Master
Source: Servant > Nature (4th Paragraph)
Servants are summoned from the Throne of Heroes with the promise of their own wish being granted and as Rin explains in the Visual Novel to Shirou, it is only the Servants who can use the Holy Grail as such Masters who want their own wish granted need to have 1 Command Spell remaining to force the Servant to grant their wish over the Servants.
Some Servant's wish is granted by being summoned such as Diarmuid Ua Duibhne who wanted to serve a lord again while with some Masters the Wish from the Grail is not their goal such as Waver who wanted to win as proof that his was as good of a Magus as they of the bloodline families while Tohsaka Tokiomi wanted to use the Grail as a means to reach The Root, not to wish for a way there. one can also suspect that the Einzberns wanted the same since that's where they would reclaim the 5th Magic.
however post 3rd Fuyuki War even if a Master or Servant had no wish from the Grail, it would default to Angra Mainyu's as his was already in the process of being granted. wishes made after that point was more Angra Mainyu using the Grail's power to grant the wish itself (ie. how the process of Kiritsugu's wish was described to him in Fate/Zero)
In the event of no Wish by anyone i would suspect the energy would be saved up and anew Holy Grail War would start sooner. this is sorta like what happened between the 4th and 5th wars yet some of that energy was spilled out in the form of the Black Mud but there was still enough to cut the wait time to the next war to less than a decade.
however the chances of no one having a wish is very very very low. Diarmuid was probably a rare case for not having a wish for after the war so there will very likely always be a Servant who would want their wish granted while Masters are actually chosen by the Grail. while the choosing process is not clear we could think that they all have to desire the Grail's use. Shirou being chosen could be explained by his ideal to be a hero