Cream were first to get drunk (7)
I believe the answer is:
Here is my best explanation:
'drunk' is the definition.
'cream were first' is the subsidiary indication.
'cream' becomes 'pick' ('pick' can be a synonym of 'cream').
'were first' becomes 'led'.
'to get' is the link.
(Other definitions for pickled that I've seen before include "Soused", "Drunk (as a gherkin?)", "Brahms and Liszt", "Preserved in vinegar or brine", "Blotto", "Preserved - drunk", "preserved in vinegar" and "Preserved in liquid".)