Edmund Mortimer, the 5th Earl of March, was the brother of Richard 3rd Duke of York's mother Anne, and was also seen by some as the rightful King of England. He died in 1425 aged 33 without issue, thus transferring his claim to the throne to his nephew Richard and the House of York, something that contributed to the War of the Roses.
What happens if he does not die in 1425, and survives into the 1450s, would he be considered a rival to Henry VI? Would he form part of a regency council? Furthermore, what might happen if he has children with his wife Anne Stafford?
Pay no attention to Shakespeare's depiction of Mortimer as a miserable prisoner of the house of Lancaster. He was a loyal vassal of Henry V from 1413, when Henry released him from the custody imposed by Henry IV, and made him a Knight of the Bath.
He did not press his claim to the throne in any way at the time of Henry VI's succession in 1422; instead he
was appointed to the Council of Regency. He quarrelled with fellow Councilor Humphrey of Gloucester, but that seems to have been purely personal.
If he had children, they, not the Yorks, would be next in line after the Lancasters. So Richard of York would not rebel, at least not in the OTL way.
I doubt if Edmund would ever raise the claim, but his son or sons might. Or if he had a daughter she might be married to Henry VI, to unite the claims and avert a possible dynastic war. (Against that is the usual practice of royal marriage to a foreign princess.)
If not, the House of Mortimer might continue for generations, separate from the House of Lancaster, yet holding a superior claim. After three or four generations, the claim might be considered to lapse by neglect, but it would be an awkward precedent.
And it could provide a rallying point for rebels or dissidents - say during the Reformation, if the Mortimers and the Crown line were of different creeds, or as an alternative to a union of crowns under the King of Scotland (as in OTL).