In short, yes. We know of many home educated children from Northern Ireland who have taken exams and gone on to higher education. The Home Ed Exams Wiki (along with the Home Ed Exams and Alternatives Facebook group) is the best place to start your research, and through our Facebook page you will be able to find other local parents who have helped their children through this for advice and support.
It can feel a bit overwhelming when you start looking into this but essentially you need to pick a subject and an Exam Board which your Exam Centre can offer. That may mean choosing an iGCSE in order to avoid coursework (which home educators can’t generally get marked). You will find information on available Centres on the Exams Wiki.
Then work out how best to approach the syllabus- this may be to study independently with textbooks or online resources and YouTube, you may use a DLP (distance learning provider) or you may sign up with a tutor or class.
Then you do the work and book the exam probably before January or February for a June sitting but check your Centre’s deadlines.
The EA published information on the promised new centre for 2021 here- https://www.eani.org.uk/services/elective-home-education#public-examinations-2021, although in the event all bookings were cancelled and the centre did not help candidates seek Centre Assessed Grades. The EA asks that queries and applications for future years are sent to EHE.Exam.Enquiries@eani.org.uk (Update 24/02/21 – https://hedni.org/2021/02/24/exam-worries/, and some thoughts on planning to take exams in 2022 and 2023 – https://hedni.org/2021/05/19/considering-exams-for-next-year/ )