The publisher has shortlisted Mother, Grey, CDP London and Karmarama to pitch for the business, which is currently held by Hurrell Moseley Dawson & Grimmer. The incumbent will not repitch.
HMDG was appointed last year to work on the title's £18 million launch programme following Shaun McIlrath's arrival as its creative director.
McIlrath, who worked with IPC at the now defunct Heresy, left HMDG last month to join Iris as its executive creative director.
HMDG continues to handle advertising for Pick Me Up, which is housed within IPC Connect, the division that publishes Look.
An IPC Connect spokesman said: "HMDG picked up the business for the initial launch phase of Look on a one-year fixed contract, which is now up. It has delivered great work, but we always intended to repitch at this point as the brand transitions from launch into the next phase of its development."