It would appear that the Inn had only 4 licensees in its history as an Inn and it was licensed for the last time in 1873. The Inn appears to have closed not long after this and for a while it was operated as a boarding house before reverting to a private residence.
The beautifully preserved Star of Tasmania Inn remains a private residence to this day.
Main Text & Information Source –
“The Story of Battery Point – Street By Street” – Donald Howatson 2012
“Here’s Cheers” – C.J.Dennison