Southern peninsula is a notoriously chilly place (7)
I believe the answer is:
siberia
'notoriously chilly place' is the definition.
'siberia' can be an answer for 'place' (I have seen 'place of exile' mean 'siberia' so perhaps 'place' could also mean 'siberia'). I'm not certain of the 'notoriously chilly' bit.
'southern peninsula' is the wordplay.
'southern' becomes 's' (abbreviation).
'peninsula' becomes 'Iberia' (peninsula including Spain and Portugal).
's'+'iberia'='SIBERIA'
'is a' acts as a link.
Can you help me to learn more?
(Other definitions for siberia that I've seen before include "Cold spot" , "Vast Asian region of Russia" , "Eastern part of Russia" , "Frozen region of former USSR noted for prison camps" , "Former place of exile for a Russian" .)