The most common and most likely answer to this crossword clue is the 10 letter word DOG-PADDLE
I've seen this crossword clue in Financial Times
D
O
G
-
P
A
D
D
L
E
Buddy explains!
The straight part
We know that "stroke" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stroke = dog-paddle.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 DOG-PADDLE mean?
DOG-PADDLE noun- A swimming stroke in the style of a dog swimming.
- To swim using the dog paddle stroke.