The most common and most likely answer to this crossword clue is the 5 plus 5 letter word BRUSH ASIDE
B
R
U
S
H
A
S
I
D
E
More clues leading to the result BRUSH ASIDE
- Ignore hurry, as in “endure”
- Interrupting someone at match, American has disregard
- Dismiss sweeper for each team
- Disregard skirmish, notwithstanding
- Reform he is absurd to ignore
- Ignore American wearing his beard stupidly
- Brusquely dismiss graduate bored by career with bank
- Bowled with urgency finding an edge to dismiss
- Disregard president holding Republican ideas wrongly
Buddy explains!

The straight part
We know that "dismiss" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case dismiss = brush aside.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.