The most common and most likely answer to this crossword clue is the 7 letter word UMPTEEN
I've seen this crossword clue in The Times
U
M
P
T
E
E
N
More clues leading to the result UMPTEEN
- Politician needs support of course within global alliance — plenty given
- In court, youngster takes in many at first — very many!
- A great many put me out — active men, ultimately
- Many an official who may call out youth
- A lot to bear with difficulty from Cockney youth
- Padded seat without ends even, a great deal
- Lots of superior chaps keeping private
- Loads of hesitation with parking by young person
- Quite a few men put out about failure, ultimately
- Lots consumed by plump teenagers
Buddy explains!

The straight part
We know that "A great many" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a great many = umpteen.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.