bicycle, car, equipment, etc.

car
Our hire car broke down after only an hour.

charge, cost
company, firm, shop (BrE)
a car hire firm
a costume hire shop

for hire (BrE, AmE)
There are boats for hire on the lake.

on hire
vehicles currently on hire

on hire from, on hire to
The equipment is on hire from a local company.

hire of
The main expense was the hire of a car.

new, recent
potential, prospective

by the day, week, etc.
What's the cost of hiring by the day?

locally
Ski equipment can be hired locally.

from
Bicycles can be hired from several local shops.

by the day
Workers were hired by the day.

can/can't afford to
The television studio couldn't afford to hire a top-notch cast.

hire and fire
Who is responsible for hiring and firing around here?

Hire is used with these nouns as the subject:
firm

Hire is used with these nouns as the object:
actor, actress, agent, alien, architect, army, assassin, assistant, attorney, auditor, bicycle, bike, bodyguard, cab, car, coach, consultant, contractor, counsel, crew, designer, detective, electrician, employee, expert, faculty, firm, helicopter, immigrant, inspector, intern, labourer, manager, mercenary, photographer, prostitute, replacement, room, ski, specialist, staff, taxi, trainee, tutor, vehicle, venue, worker