One often hailed as the new Verdi in California — British! (9)

'one often hailed' is the definition.
(as in hailing a cab)

'the new verdi in california british' is the wordplay.
'the new' is an anagram indicator.
'in' indicates putting letters inside.
'california' becomes 'ca'.
'british' becomes 'br' (abbreviation for British).
'verdi' with letters rearranged gives 'drive'.
'ca'+'br'='cabr'
'drive' inserted into 'cabr' is 'CABDRIVER'.

'as' is the link.