Rather than dealing Action Card as usual, have everyone roll the appropriate “maneuvering Trait” as listed below:
Participants draw a card for each success and raise on the maneuvering Trait roll, and keep one (usually the highest) as their Action Card. This determines not only their initiative but how well they managed to “maneuver” that particular round.
Characters who don't score at least a single success remain in the chase but get no Action Card that round.
Making a maneuvering Trait roll does not count as an action.
Savage Worlds Deluxe Edition p. 84