New heart for the world (5)
I believe the answer is:
earth
'world' is the definition.
(synonyms)
'new heart' is the wordplay.
'new' indicates an anagram.
'heart' anagrammed gives 'EARTH'.
'for the' is the link.
(Other definitions for earth that I've seen before include "Solid ground" , "Badger or fox burrow" , "Ground - globe - soil" , "underground shelter" , "cost of which is very high" .)