>emma was 16 when we last met her
>she is now apparently part of the police force
>and has risen to level of Detective
About 10 years, but just because 10 years have passed in L: Z-A, does not mean 10 years have passed in-universe as a whole (there's 10 in-universe years between RG and SM, despite a 20 year realtime gap). Best to treat Legends games as their own wee thing, related to the core games, but seemingly not beholden to its timeline progression (L: A featuring a DP protag about 5 years older than their DPPt/BDSP appearance, but taking place 100 years before the kid faced Cyrus and saved Sinnoh, roughly, with Arceus then sending its Flute to the kid's younger self in the modern era to meet It again).