Message that’s loud a mark of error (3)
I believe the answer is:
Here is my best explanation:
'message' is the definition.
'loud a mark of error' is the subsidiary indication.
'loud' becomes 'f' (A musical term**).
'mark of error' becomes 'x' (mark placed next to error, opposite of a tick).
'that's' is the link.
(Other definitions for fax that I've seen before include "means", "Transmit document", "Electronic transmission", "Transmission of exact copies of documents electronically", "Modern method of transmitting printed matter by phone" and "Means of communication".)