The most common and most likely answer to this crossword clue is the 9 letter word EXACTNESS
I've seen this crossword clue in Financial Times
E
X
A
C
T
N
E
S
S
More clues leading to the result EXACTNESS
- Attention to detail of former head about individual performance
- Insist upon head showing precision
- Rigour of head supporting old enterprise
- Precision perfomance welcomed by one-time head
- Old thespian with name for introduction of rigour and accuracy
- Rigour from former thespian with name for resistance
- Precision cutting tool tossed up and caught on head
Buddy explains!

The straight part
We know that "Precision" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case precision = exactness.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 EXACTNESS mean?
EXACTNESS noun- The state of being exact.