The most common and most likely answer to this crossword clue is the 3 plus 5 letter word BIG WHEEL
I've seen this crossword clue in The Times
B
I
G
W
H
E
E
L
More clues leading to the result BIG WHEEL
- Fair experience very popular with creep
- One very important feature of fairground
- Fair offering from a VIP?
- Old penny perhaps needed for fairground attraction
- Important person that’s going round in London
- Fair offer for a round trip
- American VIP has huge circle
- Ride with important person in the organisation?
Buddy explains!

The straight part
We know that "Fair experience" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fair experience = big wheel.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.