Any Toastmasters club in good standing can hold a speech contest. All of the resources for 5 different contests are available at Toastmasters.org. The International Speech Contest proceeds beyond the district to the international level. Other contests proceed only to the District level. Each year the District will decide what speech contests will be sponsored besides the International Contest: Evaluation, Humor, Tall Tales, or Table Topics.
The International Speech contest involves a 5-7 minute speech and is open to members who have completed the first level in any Path within the Toastmasters program. The contest starts at the club level and winner(s) proceed to the Area contest, then Division, then District, then Semi-finals, and finally the Finals. The District contest is held during the Spring Conference. The semi-finals and finals are held at the Toastmasters International Convention.
Anyone chairing an Area, Division, or District contest should consider wrapping a High Performance Leadership Project (HPLP) around those efforts. You can obtain an HPLP packet from the Toastmasters International online store. Note that doing so requires some additional lead time to begin the re-assessment and vision portions of the HPLP prior to pushing on the actual contest efforts.