annual
antiques, art, book, craft, horse (BrE), school (esp. AmE), steam (BrE)
career, job, science, trade
fun (usually funfair)
local, street
county, state (both AmE)

attend, go to, visit
have, hold, host
The city is holding its annual trade fair in May this year.

organize
She is organizing next year's book fair.

take place

at a/the fair
I bought it at a local craft fair.

be, seem
make sth
I'll give you ten pounds each to make it fair.

consider sth, think sth
I didn't think it fair that the others should be allowed to go but not me.

scrupulously, very
It's important to be scrupulously fair when grading the final exam paper.

absolutely, completely, entirely, perfectly, quite, totally
I don't care what he thinks. It seems perfectly fair to me.
That doesn't seem quite fair.

hardly, not really
It's hardly fair that I should be working while everyone else is enjoying themselves!

pretty, reasonably

to be fair
To be fair, we hadn't really spent enough time on the job.

to
That seems fair to all sides.

Fair is used with these nouns:
allocation, amount, assessment, balance, bet, bit, catch, chance, comment, comparison, compensation, competition, complexion, compromise, contest, copy, criticism, cross section, deal, degree, description, distance, distribution, division, election, estimate, exchange, fight, guess, hair, head, hearing, imitation, indication, inference, measure, number, offer, percentage, play, price, proportion, reflection, rent, representation, return, sex, size, skin, slice, summary, system, test, trade, treatment, trial, use, vote, wage, warning, weather, while, wind