The most common and most likely answer to this crossword clue is the 6 plus 9 letter word PENCIL SHARPENER
I've seen this crossword clue in The Daily Telegraph
P
E
N
C
I
L
S
H
A
R
P
E
N
E
R
More clues leading to the result PENCIL SHARPENER
- With which writer discovers new lead?
- Writer’s device for emphasising point?
- It helps writer to come to the point
- It gives more point to your writing
- With which writer makes good points?
- What might make the point for a writer?
- Article used by writer to make a point
- Device used by writer to make a point
- It’s used to make a point by a writer keen to back Descartes
- What one may resort to when there’s no point in solving
Buddy explains!

The straight part
We know that "What one may resort to when there’s no point in solving" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what one may resort to when there’s no point in solving = pencil sharpener.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.