Short answer
Look at what each department is measured on before you look at the people. Most conflict between departments comes from goals that pull against each other: sales is paid on volume, operations on cost, finance on cash. Agree on one shared goal for the work that crosses the line, name an owner for each handoff, and set a simple rule for settling disagreements before they reach the senior team.
The longer answer
When two departments keep clashing, leaders often treat it as a personality problem. Sometimes it is. More often, each side is doing exactly what it’s rewarded for, and those rewards conflict.
Three steps help. Put the conflicting goals side by side so everyone can see them. Agree which one wins in which situation. And teach the managers on both sides to raise the disagreement early, in the same meeting, instead of escalating it separately.
If the same fight keeps reaching your desk, the rule for settling it is missing.