The most common and most likely answer to this crossword clue is the 6 letter word HEARSE
I've seen this crossword clue in The Times
H
E
A
R
S
E
More clues leading to the result HEARSE
- Her SAE transported in black car?
- Last time transport picks up close to home
- Slow-moving vehicle picks up pace, finally
- . Picks up partner in car for final trip
- Man behind slow vehicle
- Picks up European car for final journey
- Tries electronic vehicle
- One strains to overtones, keen to join in
- Long vehicle picks up second of celebrities
- Tries key in car for person who’s late
Buddy explains!

The straight part
We know that "Last time transport" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case last time transport = hearse.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 HEARSE mean?
HEARSE noun- A hind (female deer) in the second year of her age.
- A framework of wood or metal placed over the coffin or tomb of a deceased person, and covered with a pall; also, a temporary canopy bearing wax lights and set up in a church, under which the coffin was placed during the funeral ceremonies.
- A grave, coffin, tomb, or sepulchral monument.
- A bier or handbarrow for conveying the dead to the grave.
- A carriage or vehicle specially adapted or used for transporting a dead person to the place of funeral or to the grave.
- To enclose in a hearse; to entomb.