Please be aware that a 301 is intended to be a permanent and should be cached by your browser. When testing a change in your configuration: after reloading the nginx configuration  test from a new private/incognito browser window.
I am wanting all https://www.my-clients-domain.com to rewrite to https://my-clients-domain.com
Then I would for starters ensure that when you redirect from plain HTTP to HTTPS, that your visitors immediately get redirected to https://my-clients-domain.com  and don't get redirected first from http://www.my-clients-domain.com to https://www.my-clients-domain.com where the immediately  get  a second redirect to https://my-clients-domain.com
Rather than a redirect with a $host parameter use the desired domain and have a concise:
server { 
        listen 80; 
        server_name my-clients-domain.com  www.my-clients-domain.com;
        return 301 https://my-clients-domain.com$request_uri;
}
Your SSL server block looks OK already.
I would expect a second block for the bare domain, that holds your web content: (Assuming that the certificate /etc/letsencrypt/live/my-clients-domain.com/ is also valid for www.my-clients-domain.com )
server {
    listen [::]:443 ssl ipv6only=on; 
    listen 443 ssl; 
    server_name www.my-clients-domain.com;
    return 301 https://my-clients-domain.com$request_uri;
    ssl_certificate /etc/letsencrypt/live/my-clients-domain.com/fullchain.pem; 
    ssl_certificate_key /etc/letsencrypt/live/my-clients-domain.com/privkey.pem;
    include /etc/letsencrypt/options-ssl-nginx.conf;
    ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; 
}
server {
    listen [::]:443 ssl ipv6only=on; 
    listen 443 ssl; 
    server_name my-clients-domain.com;
    root  /var/www/default/htdocs;
    ssl_certificate /etc/letsencrypt/live/my-clients-domain.com/fullchain.pem; 
    ssl_certificate_key /etc/letsencrypt/live/my-clients-domain.com/privkey.pem;
    include /etc/letsencrypt/options-ssl-nginx.conf;
    ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; 
}
Or slightly more concise:
server {
    listen [::]:443 ssl ipv6only=on; 
    listen 443 ssl; 
    server_name my-clients-domain.com www.my-clients-domain.com;
    root  /var/www/default/htdocs;
    if ($host = www.my-clients-domain.com) {
       return 301 https://my-clients-domain.com$request_uri;
    }
    ssl_certificate /etc/letsencrypt/live/my-clients-domain.com/fullchain.pem; 
    ssl_certificate_key /etc/letsencrypt/live/my-clients-domain.com/privkey.pem;
    include /etc/letsencrypt/options-ssl-nginx.conf;
    ssl_dhparam /etc/letsencrypt/ssl-dhparams.pem; 
}