Italian visiting England masters puzzles (7)
I believe the answer is:
enigmas
'puzzles' is the definition.
(an enigma is a puzzle or mystery)
'italian visiting england masters' is the wordplay.
'italian' becomes 'I' (abbreviation for Italian).
'visiting' is an insertion indicator.
'england' becomes 'eng' (abbreviation).
'masters' becomes 'MAs' (more than one Master of Arts graduate).
'i' put inside 'eng' is 'enig'.
'enig'+'mas'='ENIGMAS'
(Other definitions for enigmas that I've seen before include "Puzzles - mysteries" , "They're mysterious or difficult to understand" , "'Mysteries, riddles (7)'" , "Problems" , "'Puzzles, riddles (7)'" .)