... southern diner, but not with cold Peter (4)
I believe the answer is:
safe
'peter' is the definition.
(slang term)
'southern diner but not with cold' is the wordplay.
'southern' becomes 's' (abbreviation).
'diner' becomes 'cafe' (I've seen this in another clue).
'but not with' indicates named letters should be taken away.
'cold' becomes 'c' (eg on taps).
'cafe' with 'c' taken out is 'afe'.
's'+'afe'='SAFE'
(Other definitions for safe that I've seen before include "Out of harm's way" , "Free from risk" , "Unharmed" , "Locked store for money etc" , "Metal container for valuables" .)