The most common and most likely answer to this crossword clue is the 7 letter word IMPLORE
I've seen this crossword clue in The Times
I
M
P
L
O
R
E
More clues leading to the result IMPLORE
- Beg little devil to get learning
- Urgently request ancient stories of devils?
- Beg for tales of mischievous sprites?
- Scamp learning to beg
- Beg one extra place to be reserved
- Plead with troublemaker, backed by traditional knowledge
- Little rascal learning to beg
- Troublemaker takes stories to press
- Press learning of mischief?
- Beg one extra having scoffed half of plum
Buddy explains!

The straight part
We know that "to press" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to press = implore.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 IMPLORE mean?
IMPLORE verb- To beg urgently or earnestly.
- To call upon or pray to earnestly; to entreat.