The most common and most likely answer to this crossword clue is the 7 letter word DIPLOMA
I've seen this crossword clue in The Times
D
I
P
L
O
M
A
More clues leading to the result DIPLOMA
- Embassy official has no time for formal documentation
- What might confer a degree of tact when cutting cold Yankee
- Go down and see graduate getting certificate
- Drop lecturer with old degree qualification
- Peacemaker has no time for qualification
- Old map I mistook for official document
- Look married, covered by iPad-processed certificate
- Go down and see graduate getting award
- Ambassadorial jerk dropped certificate
- Award for ambassador leaving Thailand
Buddy explains!

The straight part
We know that "What might confer a degree" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what might confer a degree = diploma.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 DIPLOMA mean?
DIPLOMA noun- A document issued by an educational institution testifying that the recipient has earned a degree or has successfully completed a particular course of study.