The former Stourbridge MP and campaigner on children's issues left the trust for personal reasons on Sept 11.
Chief executive Jean Collingwood said: "We have been hugely privileged to have had Debra Shipley as our first chair and to have benefited from her wealth of political, media and campaigning experience.
"Debra has been instrumental in the trust's development and its successes to date."
The trust has not yet found a replacement for Shipley, but has said it is looking to recruit a new chair immediately, along with two more trustees.
Collingwood added: "We are now entering a new stage of implementing our strategic objectives with specific focus on the under-18s and those at potential long-term harm.
"We will be building upon our existing achievements and increasing the trust's level of activity.
"We are recruiting a new chair and additional trustees as part of this period of growth and expansion."
The Drinkaware Trust was set up at the end of last year to help bring about change in the national drinking culture, reduce alcohol misuse and minimise alcohol-related harm.