Former PM, first to enter study (4)
I believe the answer is:
eden
'former pm' is the definition.
(I've seen this before)
'first to enter study' is the wordplay.
'first to' indicates taking the first letters.
'study' becomes 'den' (I've seen this before).
The initial letter of 'enter' is 'e'.
'e'+'den'='EDEN'
(Other definitions for eden that I've seen before include "Badly need the garden" , "The first garden" , "Paradisal garden" , "The perfect garden in need" , "(Biblical) paradise" .)