Part of a country-style date (5)
I believe the answer is:
tryst
'date' is the definition.
(tryst is a kind of date)
'part of a country-style' is the wordplay.
'part of' indicates the answer is hidden within the clue.
'TRYST' is hidden in the letters of 'country style'.
(Other definitions for tryst that I've seen before include "Rendezvous with lover" , "Lovers' appointment" , "private appointment" , "Date" , "where lovers meet" .)