Dicky came to take in cold Saudi city (5)
I believe the answer is:
mecca
'saudi city' is the definition.
(I've seen this in another clue)
'dicky came to take in cold' is the wordplay.
'dicky' indicates an anagram (dicky can mean ill or non-functioning).
'to take in' means one lot of letters goes inside another.
'cold' becomes 'C' (eg on taps).
'came' anagrammed gives 'meca'.
'meca' placed around 'c' is 'MECCA'.
(Other definitions for mecca that I've seen before include "Joint capital of Saudi Arabia" , "Goal of pilgrimage" , "Pilgrimage site" , "Holy city of Islam" , "Pilgrimage destination" .)