The most common and most likely answer to this crossword clue is the 8 letter word PRESS-UP
I've seen this crossword clue in The Times
P
R
E
S
S
-
U
P
Buddy explains!

The straight part
We know that "A little exercise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a little exercise = press-up.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 PRESS-UP mean?
PRESS-UP noun- An exercise done to improve upper body strength, performed by resting on one's toes and hands and pushing one's weight off the floor.
- A push-up bra.