Deteriorate having travelled to the south of Spain (5)
I believe the answer is:
erode
'deteriorate' is the definition.
(I've seen this before)
'travelled to the south of spain' is the wordplay.
'travelled' becomes 'rode' (I've seen this in other clues).
'to the south of' says to put letters next to each other.
'spain' becomes 'e' (abbreviation for Espana).
'rode' put after 'e' is 'ERODE'.
'having' acts as a link.
(Other definitions for erode that I've seen before include "Gradually wear away" , "fragment" , "Slowly remove" , "'Deteriorate, wear away (5)'" , "Gradually destroy" .)