The most common and most likely answer to this crossword clue is the 7 letter word AROUSES
I've seen this crossword clue in Independent
A
R
O
U
S
E
S
Buddy explains!

The straight part
We know that "Inspires" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case inspires = arouses.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 AROUSES mean?
AROUSES verb- To stimulate feelings.
- To sexually stimulate.
- To wake from sleep or stupor.