The most common and most likely answer to this crossword clue is the 7 letter word PEAKING
I've seen this crossword clue in The Sunday Telegraph
P
E
A
K
I
N
G
More clues leading to the result PEAKING
Buddy explains!

The straight part
We know that "Reaching maximum" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reaching maximum = peaking.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 PEAKING mean?
PEAKING verb- To reach a highest degree or maximum.
- To rise or extend into a peak or point; to form, or appear as, a peak.
- To raise the point of (a gaff) closer to perpendicular.
- To become sick or wan.
- To acquire sharpness of figure or features; hence, to look thin or sickly.
- To pry; to peep slyly.
- The act of something reaching a peak.
- Peaky; sickly; pining