NI Protocol: The most pressing item on the agenda for any incoming DUP leader will be what to do about the Brexit Protocol.
Though unionists and loyalists say it must go, the EU and Irish government insist it will remain.
Promises from Prime Minister Boris Johnson to address unionist concerns ring hollow and now he has bigger problems on the horizon.
With unionists feeling the post-Brexit move to prevent a hard border in Ireland has cut them off from the rest of the UK, any new leader will need to form a plan to address this concerns if they want to stick around for long.
Party unity: Another challenge will be to keep the DUP together. For the last few years of Mrs Foster's leadership it sometimes felt like the party's MLAs and MPs were operating on two different wavelengths.
Party heavyweights like Sammy Wilson, Ian Paisley and Gregory Campbell appear to be able to do and say what they want, irrespective of any difficulties it may cause for their party leader. On more than one occasion Foster has squirmed while questioned on the behaviour of her errant colleagues.
DUP elders do so safe in the knowledge that no action will be taken against them.
Assembly election: One of the primary motivations for getting rid of Mrs Foster will be concern about next year's Assembly elections.
There are real fears in the DUP that Sinn Fein could become the biggest party in Northern Ireland and win the First Minister role next May.
There are also worries around the threat posed by Jim Allister and the TUV. With many unionists growing disillusioned with the DUP and UUP, Mr Allister could benefit by offering an alternative to hardliners, as the Alliance does to moderates.
While criticised as a "one-man party", Mr Allister is seen as an MLA sticking to unionist fundamentals.
Progressive issues: A divided DUP approach to issues such as LGBT rights has done Mrs Foster no favours during her tenure as leader.
DUP veterans will never accept the party shifting to a more liberal stance, while others feel that the party has invited ridicule for its out of date views.
An attempt by Mrs Foster to get MLAs to abstain on a motion on gay conversion therapy last week prompted a backlash and may have played a part in her downfall.
Consistent leadership that unites the party will be needed on such issues, though it may find itself out of step with a more liberal society.
Irish unity: Any new DUP leader will have to lead from the front on Irish unity, rather than burying their head in the sand or threatening to leave the country.
When the subject is broached the party is quick to dismiss it.
But given the wide-ranging discussions now taking place on the topic, the new leader will have a fight on their hands to prevent a border poll.
The best way to protect the Union will be to make the case for it and show people what a Northern Ireland within the UK has to offer, something the party has been accused of failing to do under Mrs Foster's tenure.