Credit America with half dead following war (7)
I believe the answer is:
crusade
'war' is the definition.
(thesaurus)
'credit america with half dead following' is the wordplay.
'credit' becomes 'cr'.
'america' becomes 'usa' ('U.S.A.' can be a synonym of 'america'**).
'with' means one lot of letters go next to another.
'half' suggests halving the letters.
'following' means one lot of letters go next to another.
'dead' halved is 'de'.
'cr'+'usa'+'de'='CRUSADE'
(Other definitions for crusade that I've seen before include "Vigorous campaign" , "Drive" , "Medieval Christian military expedition to capture the Holy Land" , "Advertising campaign" , "Action by Christians to recapture the Holy Land" .)