The most common and most likely answer to this crossword clue is the 8 letter word EXORCIZE
I've seen this crossword clue in The Daily Telegraph
E
X
O
R
C
I
Z
E
Buddy explains!

The straight part
We know that "Banish spirits" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case banish spirits = exorcize.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 EXORCIZE mean?
EXORCIZE verb- To drive out supposed evil spirits from a person, place or thing, especially by an incantation or prayer
- To rid a person, place or thing of an evil spirit