Transported quietly through desert (4)
I believe the answer is:
rapt
'transported' is the definition.
(I've seen this before)
'quietly through desert' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'through' is an insertion indicator (I've seen this in other clues).
'desert' becomes 'rat' (ratting is a kind of deserting).
'p' inserted within 'rat' is 'RAPT'.
(Other definitions for rapt that I've seen before include "Ecstatic in part" , "carried away" , "Spellbound, enthralled" , "Fully intent, fascinated" , "Completely absorbed" .)