Widespread destruction, half having started overtaking cities (5)
I believe the answer is:
havoc
'widespread destruction' is the definition.
(I've seen this in another clue)
'half having started overtaking cities' is the wordplay.
'half' means to take half the letters.
'started' suggests taking the first letters.
The first letters of 'overtaking cities' is 'oc'.
'having' halved is 'hav'.
'hav'+'oc'='HAVOC'
(Other definitions for havoc that I've seen before include "Total destruction" , "Violent and needless disturbance" , "Pandemonium" , "Ruin" , "Carnage" .)