As mentioned above this question is false by its very nature – an employment contract is in place as soon as someone begins working for you, whether it is written down or not. It is also worth noting that employment contracts can be in writing sometimes without being lengthy – if you sent a short letter or an email to an employee before they started work but there was no follow-up document, then that letter or email is effectively your written employment contract.
If you want to introduce a written contract for an existing employee, do NOT attempt to do so without first speaking to a lawyer. This contract will require appropriate fresh consideration, and the terms should not diminish the employee’s existing setup. This written agreement will provide certainty in the relationship, and can help protect the business later on if you need to let that employee go. Remember though, a new contract would put an employee in the position of signing away rights that they already have, so this must be done very carefully in order to avoid a legal claim later.