At peace, travelling round southern tip of NZ (4,4)

'tip of nz' is the definition.
(easternmost point of New Zealand)

'at peace travelling round southern' is the wordplay.
'travelling' is an anagram indicator.
'round' means one lot of letters goes inside another.
'southern' becomes 's' (abbreviation).
'at'+'peace'='atpeace'
'atpeace' anagrammed gives 'eatcape'.
'eatcape' placed around 's' is 'EAST CAPE'.