Friendship to influence half of nation (9)
I believe the answer is:
affection
'friendship' is the definition.
(thesaurus)
'influence half of nation' is the wordplay.
'influence' becomes 'affect' (I've seen this before).
'half of' suggests halving the letters.
'nation' with half the letters taken is 'ion'.
'affect'+'ion'='AFFECTION'
'to' is the link.
(Other definitions for affection that I've seen before include "Warm regard" , "Goodwill" , "Feeling of love or strong liking" , "Fondness, tenderness" , "Feeling of fondness" .)