The most common and most likely answer to this crossword clue is the 14 letter word ATTRACTIVENESS
I've seen this crossword clue in The Sunday Telegraph
A
T
T
R
A
C
T
I
V
E
N
E
S
S
More clues leading to the result ATTRACTIVENESS
Buddy explains!

The straight part
We know that "ability to draw" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ability to draw = attractiveness.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 ATTRACTIVENESS mean?
ATTRACTIVENESS noun- The state of being attractive or engaging.
- The result of being attractive.