Heads for America — Palm Springs — enjoying recess (4)
I believe the answer is:
apse
'recess' is the definition.
(apse is a kind of recess)
'heads for america palm springs enjoying' is the wordplay.
'heads for' indicates taking the first letters (I've seen 'head for' mean this).
The initial letters of 'america palm springs enjoying' is 'APSE'.
(Other definitions for apse that I've seen before include "Church recess with domed or arched roof" , "where praetor sat" , "may be seen in church!" , "Recess at eastern end of a church" , "Church's part" .)