A desert space centre in the wild West (5)
I believe the answer is:
waste
'a desert' is the definition.
(thesaurus)
'space centre in the wild west' is the wordplay.
'centre' indicates the central letters.
'in' indicates putting letters inside.
'the wild' is an anagram indicator.
The middle letter of 'space' is 'a'.
'west' with letters rearranged gives 'wste'.
'a' put within 'wste' is 'WASTE'.
(Other definitions for waste that I've seen before include "Detritus" , "Uncultivated area" , "Use carelessly" , "Use inefficiently or inappropriately" , "Refuse, garbage, rubbish" .)