Woman touring hot area north of a desert (7)
I believe the answer is:
saharan
'of a desert' is the definition.
(relating to the Sahara Desert)
'woman touring hot area north' is the wordplay.
'woman' becomes 'saran' (I am not sure about this - if you are sure you should believe this answer much more).
'touring' is an insertion indicator (touring can mean going round).
'hot' becomes 'h'.
'area' becomes 'a' (maths abbreviation).
'north' shows that the letters should be reversed in order (in a down clue, letters go up or 'northward').
'h'+'a'='ha'
'ha' backwards is 'ah'.
'saran' placed around 'ah' is 'SAHARAN'.
(Other definitions for saharan that I've seen before include "Deserter" , "Baking" , "Relating to the North African desert" .)