The most common and most likely answer to this crossword clue is the 7 letter word JOYRIDE
I've seen this crossword clue in Independent
J
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More clues leading to the result JOYRIDE
Buddy explains!

The straight part
We know that "“drive illegally”" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case “drive illegally” = joyride.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.
What does JOYRIDE mean?
JOYRIDE noun- An instance of driving a motor vehicle in a carefree or reckless manner, especially a vehicle which has been taken without the permission of the owner.
- A ride taken for enjoyment.
- To take a joyride.