Old-style resort (not southern) in trouble (5)
I believe the answer is:
retro
'old-style' is the definition.
(I've seen this in another clue)
'resort not southern in trouble' is the wordplay.
'not' is a deletion indicator.
'southern' becomes 's' (abbreviation).
'in trouble' is an anagram indicator.
'resort' with 's' taken out is 'reort'.
'reort' is an anagram of 'RETRO'.
(Other definitions for retro that I've seen before include "Looking back" , "Style derived from the past" , "Describes the style of an earlier time, in short" , "Imitative of an older style" , "Consciously old style" .)