big, deep, great, sharp
growing
north-south, etc.
class, cultural, economic, ethnic, gender, generational, ideological, political, racial, religious, sectarian, social
partisan (esp. AmE), party
digital
the digital divide between people with access to technology and those without

create
widen
policies which have widened the divide between rich and poor

close, narrow
bridge, cross, straddle
advice on bridging cultural divides
It's a friendship which crosses the divide of social class.
a style which straddles the divide between classic and modern

address
attempts to address the racial divide in this country

widen
narrow
open, open up
separate sth
a divide separating those who have access to computers and those who don't

divide between
the sharp divide between rich and poor regions

divide in
The leader's speech aimed to close the embarrassing divide in party ranks.