The most common way a chaplain is appointed is by way of recommendation by a current serving chaplain. Increasingly common is the invitation by sports administrators of ministers or ex-athletes with whom they have personal or professional relationships.
If you are looking to cut into sports chaplaincy from start, try building some relationships with officials. Get involved with your old club, start getting involved on a practical level, like a property steward, trainer, massuer, etc.
Most national sports chaplaincy organisation have a minimum ministry requirement. Find out as much as you can before making official contact with your club.