deep (esp. AmE), fervent, great
a feeling of considerable hope
It is my fervent hope that you will be able to take this project forward.

high (only used with hopes)
We have high hopes for the project.
Hopes are high that a resolution to the conflict can be found.

best, main
Privatization seems to offer the best hope for the industry.

faint, slight, vague
There was still a faint hope that they would accept the offer.

real, sincere
without any real hope of success
It is my sincere hope that she will find happiness at last.

realistic, reasonable
desperate, wild
false, forlorn, vain
He wasn't trying to give her false hope.
It seemed a forlorn hope that we would find a taxi.

dashed
early
His early hopes of freedom were now gone.

last, only
He had one last hope to cling to.

fresh, new, renewed
the treatment gave him renewed hope

sudden
Her dark eyes lit with sudden hope.

lingering (esp. BrE), remaining
These figures kill off any lingering hopes of an early economic recovery.

personal

flicker, glimmer, ray, spark
I looked at her and felt a glimmer of hope.

be full of, cherish, entertain, feel, harbour/harbor, have, hold, see
He secretly cherished hopes that George would marry his daughter.
Political leaders do now entertain the hope that a settlement can be found.
She saw little hope of meeting the targets.

express, voice
The Mexican president expressed hope for cooperation on trade.

share
pin, place, put
He pinned all his hopes on getting that job.

find
Maybe we can find some hope for humanity after all.

cling to, keep alive, live in
It is important to keep alive the hope that a peace settlement might be found.
I haven't yet found a place to rent, but I live in hope.

not hold out
I don't hold out much hope of finding a buyer.

abandon, give up, lose
I didn't give up hope of being released.

bring sb, give sb, offer (sb), provide, raise
The use of fish oil to treat cancer has brought fresh hope to millions of sufferers.
This announcement has raised hopes that the crisis may be coming to an end.

boost (esp. BrE)
The latest job figures have boosted hopes for the economy.

crush, dash, destroy, end, kill, kill off, shatter, wreck (esp. BrE)
Her hopes of going to college have now been dashed.

lie, rest
Her only hope lay in escape.
Their main hopes rest on their new striker.

grow, rise
Hopes of a peaceful end to the strike are now growing.

flare (esp. AmE), flare (AmE), spring, spring up, surge
Hope flared up inside her.

remain
Hope remains that survivors will be found.

die, disappear, fade
Hope faded after wrecked remains of the ship were washed onto the shore.

beyond hope
damaged beyond hope of repair

in hope of, in the hope that, in hopes that (AmE)
I am writing to you in the hope that you can help me obtain some information.
I am writing this letter in hopes that it will be forwarded to the editor.

without hope
She felt weak and without hope.

hope for
young people who are full of hope for the future

hope of
I have no hope of winning.

every hope of sth, little hope of sth, no hope of sth, some hope of sth
We have every hope of completing the project this year.
There is little hope that they will be found alive.

grounds for hope, reason for hope
We now have good grounds for hope.

keep your hopes up
We're trying to keep our hopes up.

not a hope in hell (informal)
You don't have a hope in hell of finding a job.

a sign of hope, a symbol of hope
not get your hopes up
I'll see what I can do, but don't get your hopes up too much.

big hopes, high hopes
They have high hopes for their children.

future
distant
Peace is a distant hope in this war-torn region.

personal
unfulfilled
a bitter tale of unfulfilled hopes

championship, medal, Olympic, play-off, title, etc.
the team's championship hopes

carry
Every time he plays he carries the hopes of the entire nation.

hope for, hope of

your hopes and dreams, expectations, fears, etc.
She told me all her hopes and dreams.

big, bright
last, one, only
He turned to her in despair and said, ‘You're my last hope.’
Our one hope was that the hurricane would change direction.

medal

represent
He represents our best hope for a swimming medal.

hope for
She is Britain's brightest hope for a medal.

hope of
The operation was Kelly's only hope of survival.