Ghastly start to genocide on border (4)
I believe the answer is:
grim
'ghastly' is the definition.
(I know that ghastly can be written as grim)
'start to genocide on border' is the wordplay.
'start to' suggests taking the first letters.
'on' is a charade indicator (letters next to each other).
'border' becomes 'rim' (both can mean an edge).
The first letter of 'genocide' is 'g'.
'g'+'rim'='GRIM'
(Other definitions for grim that I've seen before include "(Of humour) black; unappealing, depressing" , "formidable" , "Dreadful" , "Tight-lipped and foreboding" , "Serious; dour" .)