Putting aside BBC News and its Reith issues...
When will BBC Parliament get Reith, and an updated Reith Logo?
Judging how long the BBC is taking to roll this typeface out, probably never as this rate!
One would hope because its supposed to come under the BBC News umbrella it'll be rolled out at the same time.
I seem to remember when the current graphics appeared on BBC News in 2013, Parliament had their lower thirds adjusted to look similar but not quite the same as they were using the old Aston system at the time.
It was only around 2015/2016 when they inherited and installed some of the old TVC kit which ISTR included an old Viz server/engine that the graphics matched the News channel.