The most common and most likely answer to this crossword clue is the 9 letter word INCREMENT
I've seen this crossword clue in The Daily Telegraph
I
N
C
R
E
M
E
N
T
More clues leading to the result INCREMENT
- Popular building material? About right for something added on
- Popular setter secures right to get pay rise
- Step up can be nasty when moving right to left
- Small step, right into favoured building material
- Horrible Republican obscures liberal growth
- This increase would be harsh if Right were left
- Home building material – builder finally brought in a bit more
- Something added in court about people being put inside
- Hip and radius encased in plaster addition
- Rise in setter accepting bit of reward
Buddy explains!

The straight part
We know that "addition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case addition = increment.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 INCREMENT mean?
INCREMENT noun- The action of increasing or becoming greater.
- The waxing of the moon.
- The amount of increase.
- An amplification without strict climax, as in the following passage: "Finally, brethren, whatsoever things are true, whatsoever things are honest, whatsoever things are just, whatsoever things are pure, whatsoever things are lovely, whatsoever things are of good report, [...] think on these things."
- The amount of time added to a player's clock after each move.
- (grammar) A syllable in excess of the number of the nominative singular or the second-person singular present indicative.
- To increase by steps or by a step, especially by one.