Follow the sun, travelling through the heart of Greece (5)
I believe the answer is:
ensue
'follow' is the definition.
(thesaurus)
'the sun travelling through the heart of greece' is the wordplay.
'travelling' is an anagram indicator.
'through' indicates putting letters inside (I've seen this in other clues).
'the heart of' says to take the centre.
The central letters of 'greece' are 'ee'.
'sun' with letters rearranged gives 'nsu'.
'nsu' put into 'ee' is 'ENSUE'.
(Other definitions for ensue that I've seen before include "Cultivate plants/vegetables" , "Come to pass" , "Befall" , "Happen as a result, follow ( 5)" , "Transpire" .)