The most common and most likely answer to this crossword clue is the 10 letter word TACHOMETER
I've seen this crossword clue in The Times
T
A
C
H
O
M
E
T
E
R
More clues leading to the result TACHOMETER
Buddy explains!

The straight part
We know that "Cab's recording device" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cab's recording device = tachometer.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 TACHOMETER mean?
TACHOMETER noun- A device for measuring the revolutions per minute (RPMs) of a revolving shaft, as with the driveshaft of an automobile.
- A device for measuring or indicating velocity or speed, as of blood, a river, a machine, etc.