foreign, international, local, national, provincial (BrE)
gutter (BrE), mainstream, popular, quality (esp. BrE), tabloid
left-wing, liberal, right-wing
The right-wing press tried to stir up prejudice against immigrants.

financial, gay, music, etc.
free
A free press is fundamental to democracy.

alert, brief, tell
Someone must have alerted the press that she was going to be there.

meet
The president was briefed before meeting the press.

censor, muzzle
They introduced measures including muzzling the press and illegal detainment.

intimidate, manipulate, mislead
Did the senator deliberately mislead the press?

briefing, release, statement
He issued a press statement insisting on his innocence.

corps
The spokesman addressed an international press corps.

attention, coverage
extensive press coverage of the event

account, report
clippings, cuttings (BrE)
He kept a scrapbook containing press cuttings of his concerts.

office
The company's press office did not return the call.

agent, officer, secretary, spokesman
photographer
agency
badge (esp. AmE), credentials, pass
She showed the doorman her press pass.

box
We got to sit in the press box since my dad would be writing about the game.

preview, screening
campaign (esp. BrE)
freedom

in the press
There was no mention of the incident in the national press.

get a good, bad, etc. press (BrE), get good, bad, etc. press, have a good, bad, etc. press (BrE), have good, bad, etc. press
His latest novel didn't get (a) very good press (= was not praised in the media).

printing

go to
The newspaper goes to press at 6 o'clock.

roll
The presses are already rolling.

in press
Their new book is in press.

hot off the press, hot off the presses (esp. AmE)
We've just received a copy of her latest book, hot off the press.

stop the press, stop the presses (= a major event has happened)
Stop the presses! Dan has had a haircut!

firmly, forcefully, hard
She pressed down hard on the gas pedal.

gently, lightly, softly
Her lips softly pressed my cheek.

close, closely
He pressed up closer against the wall, terrified of being seen.

tightly
She curled up, her knees pressed tightly to her chest.

back, down, forward, together, up, etc.
The crowd pressed forward.
She pressed her lips together.

against
She pressed her face against the window.

into
Bella pressed her face into the pillow.

on
She pressed on the doorbell.

to
He pressed a finger gently to her lips.

press sth flat, press sth open, press sth shut
He pressed the lid firmly shut.

strongly
In the interview he strongly pressed his point of view.

consistently, continually, repeatedly
gently
‘Are you sure?’ she pressed gently.

further
successfully

continue to

for
The party will continue to press the case for a new electoral system.

on
I did not press him further on the issue.

immaculately pressed, neatly pressed
his immaculately pressed suit

with
They pressed boldly on with their plan.

press on regardless (esp. BrE)
The weather was dreadful but we pressed on regardless.

Press is used with these nouns as the object:
accelerator, attack, bell, button, buzzer, cheek, claim, demand, doorbell, hand, key, kiss, knife, lever, luck, matter, palm, pedal, point, seam, shutter, switch, trigger