The 14-year-old was stabbed to death in the 1960s but the main suspect in her killing died last year before he could be brought to court.
The High Court in London granted a new inquest this morning after the original hearing in 1966 named the wrong killer.
Her family say with a new inquest, fresh evidence can be brought to the table and they may finally get closure for her killing.
Elsie was attacked from behind and stabbed in the back and head as she walked through a railway tunnel off a canal towpath in Wakefield in October 1965.
Ian Bernard Spencer was named as her killer at her first inquest, but was never convicted.
Detectives re-investigating Elsie’s murder since 2016, were preparing to charge convicted child killer and rapist Peter Pickering after new evidence came to light, but the 80-year-old died in March 2018, after being taken ill in the secure psychiatric accommodation in Berkshire where he was held for more than 45 years.
In the week before his death, Pickering was found guilty of the violent rape of an 18-year-old woman in Sheffield in 1972.
The crime only came to light as a result of the cold case investigation into Elsie’s murder by West Yorkshire Police.
Speaking outside the Royal Courts of Justice, her brother Colin Frost described today's outcome as a "massive step in the right direction".
He said that he was "totally elated" and they had "come a long way".