The mechanism I've used for this is to allow overflow from sprint actions to function as a one-round duration penalty to sprint actions by whoever they're chasing.
So, suppose we've got a fast person (F), who always gets an athletics check result of 6, and a slow person (S), who always gets an athletics check of 4.
On round one, S runs away, and can move 4 zones. F catches up, and has two points of overflow, which applies a -2 penalty to S's next sprint.
On round two, S can only move 2 zones - he's getting hedged in and harried. F catches up again - and this time has four points of overflow, applying a -4 penalty to S's next sprint.
On round three, S can't run away; he can still try something else (like a maneuver to trip F), but F is definitely going to get some kind of action off as well.
On round four, there's no penalty in place anymore, and S can move another four zones away - essentially, this is a repeat of round one.