The SLBM version of the Gale-III missile, the SeaGale, has been launched from a submarine for the first time, albeit from a submarine on the surface and not submerged. The trials submarine CNSS Warhammer fired the test missile from a secret location on Cloneworld. The missile landed deep in the main Cloneworld ocean (said to be the designated test site).
The HCS Navy plan 3 more launches in this series, at least 2 will be with Warhammer submerged. There is still a long wait until the first dedicated ballistic missile submarine in HCSN service (the Walrus class planned to enter service from 2116) though following trials Warhammer which has 3 missile tubes will also be available for service use. A submarine launched version of CSM is definitely planned though the Clones have kept quiet about it. As CSM uses the same launcher as Gale-III/SeaGale it is likely that a submarine launched CSM isn't that far away.
