How do I check an instructor before a long plan?

Licence, DBS, insurance, first aid, and a trial class first.

Before you commit to a yearly plan, take a little time to check. A good club will not mind.

Governing body licence. Ask which governing body the instructor belongs to, and ask to see their licence or membership.
DBS. Anyone teaching children should hold a current DBS check. You can ask to see it. A DBS certificate is one part of the picture, so look at it alongside references and your own judgement.
Insurance. Ask if the club has public liability insurance.
First aid. Ask who is first aid trained.
A trial class. Go and watch, or try one lesson, before paying for a long plan.

Where you can, start with a month, not a year.