There is no official 4th XV comp.
The official AAGPS competitions are 1st XV, 2nd XV and 3rd XV competitions.
The 3rd XV competition includes the 1st XV teams from Grammar, High and TAS.
If they drop out of this competition they are not in an official AAGPS rugby competition.
It is correct that when the modern 3rd XV competition restarted in 2012, TAS, Grammar and High joined it and Newington did not, largely due to the number of teams (and other factors).
It is also correct that in recent years the Newington 3rd XV has been stronger than the High 1st XV, but the 8 teams in the 3rd XV competition have remained unchanged.