The search powers in Schedule 7 do apply for journeys between Great Britain and Northern Ireland - whether or not the person questioned had previously crossed the border with the Republic of Ireland. Indeed, they also apply to scenarios like an air journey entirely within Great Britain, featuring a questioned person who has never left the UK.
The question refers to paragraph 2 of Schedule 7 to the Terrorism Act 2000. This provides that (2(1) and (4)):
(1) An examining officer may question a person to whom this paragraph applies for the purpose of determining whether he appears to be a person falling within section 40(1)(b).
...
(4) An examining officer may exercise his powers under this paragraph whether or not he has grounds for suspecting that a person falls within section 40(1)(b).
The reference to 40(1)(b) is to whether the person "is or has been concerned in the commission, preparation or instigation of acts of terrorism". In the questioning, the person being examined must "give the examining officer any information in his possession which the officer requests" (5(a)) and it is an offence to "wilfully fail to comply" with this duty (18(1)(a)); there is a large amount of other accompanying procedure. The Schedule must be read in the context of judicial decisions such as Beghal v UK (European Court of Human Rights, application no. 4755/16, 28 February 2019) which have curtailed its applicability as written.
There is a parallel setup, structured in the same way, in Schedule 3 to the Counter-Terrorism and Border Security Act 2019; this applies instead to somebody potentially "engaged in hostile activity" rather than strictly "terrorism". See 1(5) and (6) of that schedule for the definition of "hostile activity".
The core of the question here is whether these powers could be applied for somebody travelling between Northern Ireland and Great Britain. The answer is yes. In paragraph 2 of Schedule 7, we read:
(2) This paragraph applies to a person if—
(a) he is at a port or in the border area, and
(b) the examining officer believes that the person’s presence at the port or in the area is connected with his entering or leaving Great Britain or Northern Ireland or his travelling by air within Great Britain or within Northern Ireland.
(3) This paragraph also applies to a person on a ship or aircraft which has arrived at any place in Great Britain or Northern Ireland (whether from within or outside Great Britain or Northern Ireland).
In the scenario in the question, somebody might be at an airport in NI in order to leave NI, then later be on the plane when it arrives in GB, and a little after that be inside the GB airport. All of that is in scope. The same is true for sea journeys.
The point is that 2(2)(b) is phrased as "entering or leaving Great Britain or Northern Ireland" rather than "entering or leaving the United Kingdom", and so it applies to the act of leaving NI, and to the act of entering GB. This reading may seem nitpicky but it is consistent with the scheme and history of the legislation.
The border security provisions here are descended from those in the Prevention of Terrorism (Temporary Provisions) Act 1974, which covered "the examination of persons arriving in, or leaving, Great Britain or Northern Ireland". That Act was directed at IRA terrorism in 1973-1974, which very much featured people travelling from NI to GB, rather than entering the UK from outside. The wording here is the same. Likewise, Schedule 5 of the Prevention of Terrorism (Temporary Provisions) Act 1989 is in broadly the same terms as Schedule 7 of the Terrorism Act 2000, but calls out "acts of terrorism connected with the affairs of Northern Ireland" (2(2)(a)). The powers don't make sense if they don't cover people taking a ferry from Belfast to Liverpool.
Moreover, Schedule 7 paragraph 15 says that for ships and aircraft arriving in GB from NI (among other possibilities explicitly listed), there must be arrangements for the passengers to be examined on board or at the port on either end. That provision is vacuous unless it is about an examination under paragraph 2. So the questioning powers must apply to such a scenario.
