Emphasize your top transferable skills and strengths that make you a good fit for the new industry.
I'm switching to marketing because I think it's a great fit for my strengths and interests. I'm good at managing creative teams and coming up with innovative messaging. I know you're looking for an outside-the-box thinker and able manager to spearhead your rebranding campaign, and that's who I am.
There may be aspects of this industry that have always fascinated you. Emphasize these.
I'm switching to education because I've always been drawn to teaching. Even though I've worked in other jobs, I kept finding myself drawn to mentoring and training other people, and that's why I decided to go back to school for my Masters. Now that I have my degree, I'm really looking forward to starting my career as a teacher.