If a hook is deep within the throat, cut the line as close to the hook as possible this causes less damage than removing a deeply-set hook. Most fish are able to reject the hook or the hook dissolves over time.
Keep the fight short. Long fight times result in an exhausted tarpon, which is more vulnerable to predators.
Use tackle that matches the fish and conditions.
Since predators can decrease survival of fish after release, when predators become abundant and appear to be attracted to your fishing activity, consider moving to another fishing location.
If a shark appears while you are fighting a tarpon, break the tarpon off so it has a chance to escape the shark before it is too tired.