Judge new bishop in old Yorkshire city to be an archetypal Englishman (4,4)
I believe the answer is:
john bull
'an archetypal englishman' is the definition.
(figure personifying England or the UK)
'judge new bishop in old yorkshire city' is the wordplay.
'judge' becomes 'j' (abbreviation for judge).
'new bishop' becomes 'nb' (this might be a standard abbreviation of which I'm unaware).
'in' is an insertion indicator.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'yorkshire city' becomes 'Hull'.
'o'+'hull'='ohull'
'nb' put inside 'ohull' is 'ohnbull'.
'j'+'ohnbull'='JOHN BULL'
'to be' acts as a link.
(Other definitions for john bull that I've seen before include "A typical Englishman of taurine type" , "England personified" , "Typical Englishman, sign Taurus" , "Prototype Englishman" , "Traditional taurine image of England" .)