The most common and most likely answer to this crossword clue is the 4 letter word ANNA
I've seen this crossword clue in Independent
A
N
N
A
More clues leading to the result ANNA
- Siam visitor from Japan — Nagasaki
- Article that reflects historic change in India
- Woman from Clackmannan
- Girl who may turn up?
- Animated princess polished off starter of divine food
- Some vegetarian naan bread once seen in India
- Records of events lost pounds and shillings – and this
- Girl, last one on earth, found in seconds?
- She‘s writing a reflective article
- Old coin from an Asian nation
Buddy explains!

The straight part
We know that "Karenina" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case karenina = anna.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 ANNA mean?
ANNA noun- A unit of currency in former British India equal to 12 pies or 1/16 rupee.