Former partner leaving exotically unusual place (8)
I believe the answer is:
locality
'place' is the definition.
(thesaurus)
'former partner leaving exotically unusual' is the wordplay.
'former partner' becomes 'ex' (an ex-partner).
'leaving' is a deletion indicator.
'unusual' is an anagram indicator.
'exotically' with 'ex' taken away is 'otically'.
'otically' anagrammed gives 'LOCALITY'.
(Other definitions for locality that I've seen before include "Area, neighbourhood" , "Surrounding region" , "Position; area" , "Neighbourhood or site of something" .)