ADFS

The very first step to both ADFS and ADFS-Proxy is to install the new certificate.
Double-click to launch the wizard, Open MMC and copy the thumbprint

Adfs service account

In the ADFS-server. Right click on the certificate, go to Manage Private Keys

Add the read permission

With ADFS-Management Console

Open ADFS Management Console.
Go to Certficates

Select Set-Service Communications

Follow the wizard, click to view properties

Go to details and check if thumbprint matches the new one.

With Powershell

Set-AdfsCertificate -Thumbprint "" -CertificateType Service-Communications -Verbose Restart-Service adfssrv Set-AdfsSslCertificate -Thumbprint "" -Verbose Restart-Service adfssrv netsh http show sslcert

ADFS-Proxy

With Remote Access Management

Open Remote Access Management Console
Go to selected Published Web Application, and click on Edit

Click In ”External Certficate”, select the new on, Click on View and see if the thumbprints matches.

Powershell

Configure the WAP service for the new certificate.
Set-WebApplicationProxySslCertificate -Thumbprint ""

Re-establish the proxy trust
Install-WebApplicationProxy -CertificateThumbprint "UseTheNewPublic Cert Thumbprint in YOUR ADFS Server" -FederationServiceName sts.youradfsservice.com

Change the WAP published App certificate
Get-WebApplicationProxyApplication | Set-WebApplicationProxyApplication -ExternalCertificateThumbprint ""

ADFS – Change Service Communication certificate