Relative beginning to explore in French city (5)
I believe the answer is:
niece
'relative' is the definition.
(niece is a kind of relative)
'beginning to explore in french city' is the wordplay.
'beginning to' says to take the initial letters.
'in' means one lot of letters goes inside another.
'french city' becomes 'Nice' (Nice is a French city).
The initial letter of 'explore' is 'e'.
'e' placed into 'nice' is 'NIECE'.
(Other definitions for niece that I've seen before include "member of different generation" , "Daughter of a sibling" , "Criminal" , "A sibling's daughter" , "Family relative" .)