A polite sort, eager to start recess (4)
I believe the answer is:
apse
'recess' is the definition.
(apse is a kind of recess)
'a polite sort eager to start' is the wordplay.
'to start' says to take the initial letters.
The first letters of 'polite sort eager' is 'pse'.
'a'+'pse'='APSE'
(Other definitions for apse that I've seen before include "space for altar" , "Offshoot from the choir, nave or aisle in a church" , "Domed section of a church" , "Part of a church with the altar" , "room for an altar" .)