Recess well over prior to the end of June (4)
I believe the answer is:
apse
'recess' is the definition.
(apse is a kind of recess)
'well over prior to the end of june' is the wordplay.
'well' becomes 'spa' (both can mean a spring or water source).
'over' shows that the letters should be reversed in order.
'prior to' is a charade indicator (letters next to each other).
'the end of' indicates one should take the final letters.
The final letter of 'june' is 'e'.
'spa' written backwards gives 'aps'.
'aps'+'e'='APSE'
(Other definitions for apse that I've seen before include "Architectural feature in a church" , "Niche in church" , "In sacred space" , "space for altar" , "Domed section of a church" .)