great, major
bitter, brutal, serious, violent
escalating, increasing
constant, continued, continuing, ongoing
long-running, long-standing, prolonged, protracted
unresolved
He is in constant conflict with the authorities.

open, overt
global, internal, international, interstate, regional
armed, military
domestic, family, generational, interpersonal (esp. AmE), marital (AmE)
civil, class, cultural, ethnic, industrial, political, religious, sectarian, social
future, impending, potential
Our ability to mobilize large numbers of trained men in time of emergency could forestall future conflict,

bring sb/sth into, cause, come into, create, lead to, provoke
His work brought him into conflict with more conventional scientists.
The decision led to a bitter conflict between the management and unions.

avert, avoid, prevent
They hid their feelings to avoid conflict.

handle, manage
There is more to a successful relationship than simply managing conflict.

end, resolve, settle, solve
The UN are hoping to resolve the conflict quickly.

arise (from sth), occur
The conflict arose from different ambitions within the team.

erupt, flare up
rage
escalate, intensify
revolve around sth
begin, end

during a/the conflict, in a/the conflict
Thousands have been arrested in violent ethnic conflicts in the region.

in conflict
They found themselves in conflict over the future of the company.

in conflict with
in conflict with management

conflict about, conflict over
a conflict over ownership of the land

conflict between
conflicts between different ethnic groups

conflict with
to end the conflict with France

conflict within
serious conflicts within the ruling party

an area of conflict, a source of conflict
in direct conflict with sb

fundamental, irreconcilable, serious, sharp
direct
inherent
the inherent conflict between what farmers and environmentalists want

inner
emotional, ideological
personality

situation
management, resolution
the key to successful conflict management

avoidance

in conflict with
in direct conflict with his wishes

conflict between
the conflict between science and religion

conflict of
a serious conflict of opinion

a conflict of interest, a conflict of interests (esp. BrE)
a conflict of loyalties