The most common and most likely answer to this crossword clue is the 7 plus 3 letter word CLASSIC CAR
I've seen this crossword clue in Independent
C
L
A
S
S
I
C
C
A
R
Buddy explains!
The straight part
We know that "outdated conveyance" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case outdated conveyance = classic car.The cryptic/wordplay part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.