Shore leave at last privately given by head of state (7)
I believe the answer is:
seaside
'shore' is the definition.
(seaside is a kind of shore)
'leave at last privately given by head of state' is the wordplay.
'at last' suggests the final letters.
'privately' becomes 'aside' (I've seen this before).
'given by' means one lot of letters go next to another.
'head of' suggests taking the first letters.
The last letter of 'leave' is 'e'.
The initial letter of 'state' is 's'.
'e'+'aside'='easide'
'easide' put after 's' is 'SEASIDE'.
(Other definitions for seaside that I've seen before include "A place on the coast" , "Beach holiday resort area" , "Coastal area" , "Holiday destination" , "holiday venue" .)