Leave extremely desirable region (6)
I believe the answer is:
depart
'leave' is the definition.
(I know that leave can be written as depart)
'extremely desirable region' is the wordplay.
'extremely' suggests removing the centre (only the extremes of the word are used).
'region' becomes 'part' (synonyms).
'desirable' with its centre removed is 'de'.
'de'+'part'='DEPART'
(Other definitions for depart that I've seen before include "Make an exit" , "Go away; deviate" , "Prated (anag.)" , "Quit" , "Petard (anag.)" .)