This desert used to be part of Texas (5)
I believe the answer is:
waste
'this desert' is the definition.
(I've seen this in another clue)
'used to be part of texas' is the wordplay.
'used to be' becomes 'was' (eg 'he was...' means 'he used to be...').
'part of texas' becomes 'te' (I can't explain this - if you can you should give a lot more credence to this answer).
'was'+'te'='WASTE'
Can you help me to learn more?
(Other definitions for waste that I've seen before include "Spend to no purpose" , "Barren area; rubbish" , "kill" , "Use carelessly" , "''.... not, want not''" .)