Green’s Dictionary of Slang

(Aus.) a drinking glass of the largest size.

1880		Bulletin (Sydney) 11 Dec. 4/3: ‘Long sleevers,’ or pints of beer, are known as ‘Bishop Barkers’.
1972		B. Wannan Folklore of the Aus. Pub 124: Bishop Barker: a long glass of beer (now obs.).
1999		(ref. to mid–late 19C) G. Seal Lingo 30: A long glass of beer was known from the mid-19th to the late 19th century as a bishop barker, after a very tall Sydneyside cleric.