She's a month at the eye centre (4)
I believe the answer is:
mary
'she's' is the definition.
'a month at the eye centre' is the wordplay.
'a month' becomes 'mar' (short for March).
'at' is a charade indicator (letters next to each other).
'centre' means to look at the middle letters.
The central letter of 'eye' is 'y'.
'mar'+'y'='MARY'
(Other definitions for mary that I've seen before include "Successor to Edward VI" , "See 2" , "could be Wesley" , "-- Queen of Scots" , "feature of 21/23 [NATIVITY SCENE]" .)