The most common and most likely answer to this crossword clue is the 6 letter word ASPIRE
I've seen this crossword clue in The Times
A
S
P
I
R
E
More clues leading to the result ASPIRE
- Aim revealed by creature with venom and anger
- What church often has to hope
- Have lofty aims in reforming Persia
- Hope that you may find in church?
- Aim high with exceptional praise
- Short Persian jockeys have ambition
- Dream about Persia
- Hope for quiet when anger’s over
- Hope rage pursues poisoner
- Hope for a place at Oxford?
Buddy explains!

The straight part
We know that "have ambition" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case have ambition = aspire.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 ASPIRE mean?
ASPIRE verb- To have a strong desire or ambition to achieve something.
- To go as high as, to reach the top of (something).
- To move upward; to be very tall.