Check whether the interviewers have read your application or your CV/covering letter, what they already know about you. It's increasingly common for companies to do 'blind recruiting' in the shortlisting and interviewing stage, so someone shortlisting won't necessarily know your personal details, but also interviewers might not have seen your application form/CV and covering letter, so that they can compare and judge all applicants equally in response to a set of standard questions.
Basically, don't assume they are already aware of all your experience and skills. I think know I've made that mistake in the past, assuming a certain knowledge level about me on their part, when they didn't know anything except my name and the time of my interview.
This is especially common in organisations that use the STAR technique for applications/interviewing, where they'll start each interview with a template containing standard questions for all candidates and boxes to write your answers in, and then they score all candidates answers in the same way.
So don't assume they know what your previous roles were and how much experience you've got and what your skills are, what software packages you've used that are relevant to the role, etc.
Refresh your memory about the job description/person specification.
If it's over the phone, make sure you have notes to refer to it they ask any questions along the lines of 'So tell us how you would reach the different audiences for book/author X and book/author Y, what would you do differently for those marketing campaigns?' or if they say 'Tell us an example of when you briefed a creative/designer or managed a budget,' have examples ready.
Basically, have bullet points in your notes with examples of how you meet all the different criteria. And if you don't have any relevant examples from your current role or roles in that sector, think of other examples, eg, I haven't managed a budget for a marketing campaign, but I have managed a £xxk budget for a house renovation project, getting quotes, sourcing suppliers and materials, creating and sticking to a timeline, liaising with contractors and suppliers, dealing with external delays and technical problems, using my judgement to juggle and keep within costs, using a contingency and/or revising other elements of the budget, knowing what are the essentials and the 'nice to haves', what can be trimmed or cut without compromising the project.
Even if you don't have specific examples/experience of Task A, B, or C in your sector, make sure you can give them an example of how you meet that criteria, whether it's from a different sector or personal life, eg household or hobby or volunteering, such as I haven't promoted an event in my publishing roles, as I've worked on the editorial side, but when I was... I dunno? could be something like 'When I was involved in a campaign to save some trees/a community garden in my neighbourhood, another neighbour who was a whizz with graphic design created publicity materials, I put up posters, delivered flyers, (recruited other volunteers to deliver flyers), I organised a workshop and we made a banner, wrote a press release and got it covered by the local paper, I spoke in public at a council meeting on behalf of the local residents, promoted the event on different social media channels, and the campaign was successful, we saved the community garden! etc.' or could be promoting/marketing a community choir concert, or something else. Think up some more examples now, so you don't get thrown/stuck in the interview.
I always try to think of two or three examples of each skillset/scenario, because I have been thrown in the past depending on how they ask questions, when I think 'Argh! I thought that last question was the one about teamwork, but it must've been about organisational/logistical stuff/managing priorities when working with different people in different places, so I've now already used my best 'example of being good at teamwork' answer to that last question!' and if I had just had one perfect answer to the question about xyz I could've been thrown (for which, read 'have been thrown' and left umming and ahhing, trying to think up another example on the spur of the moment).
I think assuming a knowledge base about me is where I've gone wrong in a number of 'fair format' interviews, thinking I didn't want to just parrot stuff that I'd already put in my application. But I think you have to approach interviews like a clean slate nowadays, don't rely on them knowing anything about you or your previous experience, because I think these types of interviews are increasingly common.
And what you mentioned about it being hard to recruit people with knowledge of the sector. Hammer home your USP in this respect. Has the role been re-advertised? What's the skills/knowledge gap that they're looking to fill? Make sure they know you can fill it, because xyz.
And have your answers ready for 'You've been working on X side of this sector for a few years now, why do you want to move over to communications/ marketing?' make sure your answer isn't along the lines of 'I've reached a bit of a career dead-end, advancement from my current role is a 'dead man's shoes' type scenario and those people aren't going anywhere!' or 'I got on well with my previous boss, but my current boss is awful/a bully!' Always give positive reasons for wanting to make the transition, (even if you're wanting to escape in whole or in part for negative reasons), explain how and when current or previous roles have touched on this aspect and piqued your interest, any internal training you've done, or online courses, stuff done in work or in your own time, emphasising your ability to learn new skills and progress.
And don't forget to research the company and also try to think up some questions. I think my last interviewer was surprised when she asked me what I knew about them and I mentioned I'd read they'd recently received some venture capital funding and planned to triple their size. Maybe not everyone thinks about or researches the wider company and not just the role? If they're already operating, or planning to expand into, overseas territories, do you have any relevant experience, language skills, etc?
And good luck!