Travelling post-haste, gent short of time may do this? (4,2,3,3)

I believe the answer is:

step on the gas

I'm a little stuck... Click here to teach me more about this clue!

'time may do this?' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'travelling post-haste gent short' is the wordplay.
'travelling' indicates an anagram.
'short' means to remove the last letter.
'post'+'haste'+'gent'='posthastegent'
'posthastegent' with its last letter taken off is 'posthastegen'.
'posthastegen' with letters rearranged gives 'STEP ON THE GAS'.

'of' is the link.

Can you help me to learn more?

(Other definitions for step on the gas that I've seen before include "Drive faster" , "Speed up" , "Hurry" .)

I've seen this clue in The Times.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.