The most common and most likely answer to this crossword clue is the 4 letter word ERGO
I've seen this crossword clue in The Daily Telegraph
E
R
G
O
More clues leading to the result ERGO
Buddy explains!

The straight part
We know that "accordingly" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case accordingly = ergo.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 ERGO mean?
ERGO adverb- Consequently, therefore, thus.
- Therefore (especially in syllogisms).
- An ergometer (rowing machine).