Generally speaking, you don't need a certificate in an ordinary fitness club. What they care about is the quality of your teaching, or whether you can make their members happy and improve their health and quality.

Many exercises don't pay much attention to certificates. As mentioned above, the quality and feeling of members are the most important. If you have high professional standards and certificates, but the members of the club don't like you, you will be fired soon. If you don't have a certificate and your professional level is average, but you can communicate well with members and make them happy, then your popularity will be higher and higher.