The singer - real name Pippa Brown - is seen tied up in the boot of a car in the clip, which premiered online earlier this week.
'Sunday Drive' - out May 20 - is the second single from Brown's forthcoming album Anxiety, which is released on May 28.
The track follows up 'Black, White & Blue', which was put out earlier this year.
Discussing the delay of her upcoming LP, which was originally due to come out in March, the star recently told Digital Spy: "Believe me, it's been a massive pain in my arse. This album has been done for a while now but I guess the record company want it to have the best chance possible.
"I've only just come back to England so I think they want me to do a lot more promo."
> Ladyhawke confirms new album 'Anxiety' tracklisting
Watch the 'Sunday Drive' music video below: