The most common and most likely answer to this crossword clue is the 7 letter word PUBERTY
I've seen this crossword clue in The Guardian
P
U
B
E
R
T
Y
Buddy explains!

The straight part
We know that "Development of teenager" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case development of teenager = puberty.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 PUBERTY mean?
PUBERTY noun- A developmental phase brought about by the action of hormones as part of the maturing process. For humans, there are three in total.
- The age at which a person is first capable of sexual reproduction.
- The period when a plant begins to flower.