Desert island covered by rising swamp (4)
I believe the answer is:
gobi
'desert' is the definition.
(I know that Gobi is a desert)
'island covered by rising swamp' is the wordplay.
'island' becomes 'i' (geographical abbreviation).
'covered by' says to put letters next to each other (on top of in a down clue).
'rising' is a reversal indicator (going up in a down clue).
'swamp' becomes 'bog' (both can mean a wet or marshy area).
'bog' reversed gives 'gob'.
'i' after 'gob' is 'GOBI'.
(Other definitions for gobi that I've seen before include "Sandy area" , "Desert of central China" , "Plain" , "vast arid expanse" , "Mongolian expanse" .)