The most common and most likely answer to this crossword clue is the 8 letter word ADDITION
I've seen this crossword clue in The Daily Telegraph
A
D
D
I
T
I
O
N
More clues leading to the result ADDITION
- Extra problem with drugs, when losing heart
- Extra commercial issue, not first
- Something put on caught out of harmful habit
- A job for the summer
- Supplement dependency about to be got rid of
- ‘Thing’ minus 100 as an arithmetical process
- Attachment or obsession, getting caught out
- Dependence with no source of codeine supplement
- Supplement that could make pet petition?
- Dependency with no source of cash is a plus
Buddy explains!

The straight part
We know that "plus" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case plus = addition.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 ADDITION mean?
ADDITION noun- The act of adding anything.
- Anything that is added.
- The arithmetic operation of adding.
- A dot at the right side of a note as an indication that its sound is to be lengthened one half.
- A title annexed to a person's name to identify him or her more precisely, as in "John Doe, Esq.", "Robert Dale, Mason", "Thomas Way, of New York".
- Something added to a coat of arms, as a mark of honour; opposed to abatement.