The most common and most likely answer to this crossword clue is the 7 letter word WANNABE
I've seen this crossword clue in Financial Times
W
A
N
N
A
B
E
More clues leading to the result WANNABE
- A new ban upset one aspiring to greatness
- Hopeful embargo will be lifted in fall
- We must hold girl back at first, potential starlet
- Ambitious type Soubry and bishop caught by the Eye
- Shrink round collar of postulant
- Nick’s in decline, but hopeful
- Hopeful to swipe pale dresses
- Ambitious type with flag holding bar up
- Aspirant having to take in decline
- We have a girl - a born parvenu
Buddy explains!

The straight part
We know that "postulant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case postulant = wannabe.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 WANNABE mean?
WANNABE noun- Someone who wishes to be or do something, but lacks the qualifications or talent; an overeager amateur; an aspirant.
- Someone who wishes to be part of, or to assimilate to, a majority group of which they are not a member.