Oxygen needed in incredibly big desert (4)
I believe the answer is:
gobi
'desert' is the definition.
(I know that Gobi is a desert)
'oxygen needed in incredibly big' is the wordplay.
'oxygen' becomes 'O' (atomic symbol for oxygen).
'needed in' indicates putting letters inside.
'incredibly' indicates an anagram.
'big' is an anagram of 'gbi'.
'o' going inside 'gbi' is 'GOBI'.
(Other definitions for gobi that I've seen before include "East Asian desert" , "Mongolian/Chinese desert" , "Dry spot" , "Mongolian expanse" , "Large desert plateau of southern Mongolia and northern China" .)