His personality isn't specified, but it can be assumed that he is grumpy and unpleasant to be around, judging by his name.
Uncle Grump has not yet been physically shown in the series.
He gave Glummy Glooma his gloom scepter for his 1,000,000th birthday.
It hasn't been established if Grump is related to Rainbow King or not. Given that Glummy says "my uncle" to the King (rather than "our uncle" or "your dad", for example) he may only be related to Glummy through whichever parent is not a sibling of one of Rainbow King's parents.