Aristocrat baby killer Constance Marten has been granted permission to appeal her sentence, the Daily Mail can reveal.The 39-year-old is currently serving a 14-year jail term after being convicted of the gross negligence manslaughter of newborn daughter Victoria while on the run from authorities.Marten and her convicted rapist partner Mark Gordon were in hiding to prevent their baby being taken into care – something which had happened to their previous four children.But the seven-week nationwide manhunt came to a tragic end when they were arrested in Brighton in February 2023.The baby's decomposing remains were found in a shopping bag in a shed nearby two days later. It is believed Victoria died while they were sleeping in a tent in icy conditions.Marten and Gordon were convicted following a re-trial at the Old Bailey last year.But Marten has now been granted permission to appeal the 14-year sentence, the Mail has learned.She has also renewed her application to the courts for permission to appeal her conviction for gross negligence manslaughter, having already lodged at least one application some time ago. Constance Marten is appealing her sentence for gross negligence manslaughter over the death of her baby Victoria Marten caught on CCTV while she was on the run with their baby It is not known the grounds on which Marten is seeking a reduction in her sentence, nor why she has seemingly restarted the process to have her conviction quashed, and on what basis.No date has been set for any future court appearance.Sentencing the pair last September, Judge Mark Lucraft KC said their offending was made worse because the baby was vulnerable and the defendants failed to listen to past warnings.He told the defendants: 'It is clear throughout the period neither of you gave much or any thought for the care or love for your baby.'The judge said they had displayed 'arrogance' and treated Victoria to 'neglect of the most serious type'.Marten and Gordon were each also handed sentences of five years for perverting the course of justice, and 18 month terms for concealing the birth of a child, and child neglect.All sentences were concurrent with each other, and with the 14-year term for manslaughter.Police had launched a nationwide hunt after their car burst into flames on a motorway near Bolton, Greater Manchester, on January 5 2023.The defendants travelled across England and went off-grid, sleeping in a tent on the South Downs where baby Victoria died days later. Her lover Mark Gordon was also jailed, after the pair went on the run