Big cheese from Italy to follow starter of eggs (4)
I believe the answer is:
doge
'big cheese from italy' is the definition.
(type of historical Venetian magistrate)
'follow starter of eggs' is the wordplay.
'follow' becomes 'dog' (I've seen this before).
'starter of' says to take the initial letters.
The initial letter of 'eggs' is 'e'.
'dog'+'e'='DOGE'
'to' acts as a link.
(Other definitions for doge that I've seen before include "Chief of ancient Venice" , "Venetian chief magistrate" , "Venetian leader" , "Venetian ruler" , "Historically, the chief magistrate of Venice or Genoa" .)