Here's one interpretation, expressed in a series of points.
The concept of truce cannot be separated from that of war, though it lacks war's defining characteristics and is in many ways its opposite.
Fishing is something like a sport, but it lacks the aggressive characteristics of most competitive sports.
The word truce can mean both the state of truce or the act of bringing that truce about.
The phrase 'a truce to sport' could refer to the specific moment being described above, the pastime of fishing, or possibly the casting of the speakers line (casting it as a symbolic gesture).