Date an Italian chef regularly (7)
I believe the answer is:
romance
'date' is the definition.
(date can mean to woo or romance)
'an italian chef regularly' is the wordplay.
'an italian' becomes 'roman' (someone from Rome).
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'chef' are 'ce'.
'roman'+'ce'='ROMANCE'
(Other definitions for romance that I've seen before include "Sentimental affair in Menorca" , "fairy story?" , "Various languages such as French" , "Love affair; medieval tale" , "mysterious quality" .)