fierce, intense, mortal
armed, unarmed
close, hand-to-hand
open
single
active, actual
modern
ground, land, urban
aerial, air, air-to-air

be engaged in, be locked in, engage in
The troops were locked in hand-to-hand combat.

see
Our platoon has yet to see combat.

send sb into

mission, operation
zone
force, patrol, troops, unit
veteran
aircraft, vehicle
boots, equipment, fatigues, gear, jacket (BrE), suit, uniform
capability, effectiveness, power, readiness
action, experience

in combat
He was killed in combat.

in combat with
The soldiers are in combat with rebel forces.

combat against
in mortal combat against dragons

combat between
a fierce combat between two champions

effectively, successfully
She argued that the only way to combat inflation effectively was to keep interest rates high.

help (to)
be designed to

action to combat sth, efforts to combat sth, measures to combat sth, policies to combat sth
Measures to combat violent crime have been proposed.

Combat is used with these nouns as the object:
alcoholism, boredom, corruption, crime, discrimination, disease, disorder, effect, epidemic, evil, fatigue, HIV, illness, infection, inflation, menace, pollution, poverty, problem, racism, recession, spread, terror, terrorism, truancy, unemployment, vandalism