Look around Palestinian region endlessly and dream (8)
I believe the answer is:
stargaze
'dream' is the definition.
('stargaze' can be a synonym of 'dream')
'look around palestinian region' is the wordplay.
'look' becomes 'stare' (stare is a kind of look).
'around' means one lot of letters goes inside another.
'palestinian region' becomes 'gaz' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'stare' going around 'gaz' is 'STARGAZE'.
'endlessly and' acts as a link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for stargaze that I've seen before include "Study horoscope" , "looking up to our luminaries?" , "what astrologers do?" , "Look at the heavens" , "Watch the heavens" .)