You can connect arcs by having them either help or hinder each other at different points in the story. Progress in one arc might help progress another arc, or instead it might present an obstacle.
Look at Star Wars. There are 3 arcs:
1) Find the death star plans > get them to the rebels > destroy the death star
2) Han is a jerk and only cares about money > Han starts to care about Luke and Leia > Han comes back in the nick of time to save Luke
3) Luke wants to be a Jedi like his father > Obi-wan teaches him stuff about the force > After being saved by Han, Luke uses the force to destroy the death star
In parts of the movie, the arcs work against each other. Han leaving after getting his reward is a setback for the "destroy the death star" arc. When they are on the death star and Luke wants to save Leia, Han's arc makes him refuse, but then Luke uses that against him. He promises that Han will get a big reward, thus aligning the two goals.
Both Han changing (the payoff of his arc) and Luke learning to trust the force (the payoff of Luke's arc) happen right before Luke destroys the death star (the payoff of the story arc).
Here are a couple videos which may help to better visualize it: