The most common and most likely answer to this crossword clue is the 7 letter word PULL-UP
I've seen this crossword clue in Independent
P
U
L
L
-
U
P
More clues leading to the result PULL-UP
Buddy explains!

The straight part
We know that "Bit of exercise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case bit of exercise = pull-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 PULL-UP mean?
PULL-UP noun- An exercise done for strengthening the arms and back in which one lifts one's own weight while hanging from a bar.
- A pullup resistor.
- To do a pull-up or pull oneself up similarly.