Is the cancer likely to recur following treatment? What steps can I take to reduce the risk of additional new melanomas?

Frequent skin checks. Indeed having a personal history of melanoma increases your risk of developing a second melanoma. Statistics have shown at least nine times higher risk than the general population, approximately 11% will develop a second melanoma in 5 years. The 2nd tends to be at an earlier stage likely because of close observation, again highlighting the importance of frequent routine skin checks.
Protection/Detection. Protect your skin from any further sun damage! cover up to avoid sun exposure if possible. Also make sure you use sunscreen. Apply early in the day, and reapply often. Make sure you also follow up as scheduled with your dermatologist for routine full body surveillance for recurrence and/or new skin cancers.
Avoid UV Radiation. The best way to reduce the risk of new melanomas is to limit your exposure to uv radiation. Wear sun proof clothing, wear sunscreen on sun exposed areas. Never use a tanning bed. And remember to see your dermatologist on a regular basis to detect and new lesions.