Big problem with old desert (4)
I believe the answer is:
gobi
'desert' is the definition.
(I know that Gobi is a desert)
'big problem with old' is the wordplay.
'problem with' indicates an anagram.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'big' anagrammed with 'o' makes 'GOBI'.
(Other definitions for gobi that I've seen before include "Area of sand" , "barren tract" , "Large Far Eastern desert" , "Asiatic barren plateau which means 'stony desert'" , "Sandy area" .)