Buyer connects with Supplier site via Ariba Network. Thus AN is the one which does the handshake by establishing the connection and send/receive the information from Supplier site. Recently Ariba has updated all their security protocol to TLS 1.1 & 1.2 and supports communication on SSL,TSL 1.1 & 1.2. Thus if the supplier is updating their certificate and using the same widely accepted transport protocol (SSL/TLS) then there should not be any thing required on Buyer/Network side.
However you can further contact Ariba support to get currenlty supported security protocol matrices and also with supplier to know as what certificate they are updating and which protocol using for the communication.
Hope that helps!!