Cold more agreeable back in uninhabited Phuket region (8)
I believe the answer is:
'region' is the definition.
(precinct is a kind of region)
'cold more agreeable back in uninhabited phuket' is the wordplay.
'cold' becomes 'c' (eg on taps).
'more agreeable' becomes 'nicer' (nice can mean agreeable).
'back' says the letters should be written in reverse.
'in' indicates putting letters inside.
'uninhabited' suggests removing the centre (remove letters inhabiting the middle of the word).
'phuket' with its centre taken out is 'pt'.
'cnicer' backwards is 'recinc'.
'recinc' inserted inside 'pt' is 'PRECINCT'.
(Other definitions for precinct that I've seen before include "American police division" , "Enclosed space around, eg, a cathedral" , "Area with set boundaries (for pedestrians, say)" , "Designated area of US police" , "Town shopping area" .)