Was Lawrence in the desert? (5)
I believe the answer is:
waste
'the desert?' is the definition.
(I've seen this in another clue)
'was lawrence' is the wordplay.
'lawrence' becomes 'TE' (initials of TE Lawrence aka Lawrence of Arabia).
'was'+'te'='WASTE'
'in' acts as a link.
(Other definitions for waste that I've seen before include "Use inefficiently or inappropriately" , "desert" , "Blue" , "Rubbish, barren land" , "Detritus" .)