The most common and most likely answer to this crossword clue is the 2 plus 2 plus 4 letter word GO BY TAXI
I've seen this crossword clue in Financial Times
G
O
B
Y
T
A
X
I
Buddy explains!
The straight part
We know that "to eschew public transport" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to eschew public transport = go by taxi.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.