National Prime Minister twice having day out (7)
I believe the answer is:
israeli
'national' is the definition.
(I've seen this before)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for israeli that I've seen before include "Country-dweller" , "Relating to a Mediterranean nation" , "Inhabitant of Tel Aviv, say" , "Native of Middle East state" , "SW Asian" .)