Does HIV have a cure or are they close to finding one?

No cure yet. Hiv infection can be suppressed by effective antiretroviral therapy . However, no cure yet. Vaccine also not very effective as of now.
Getting closer. Treatment of HIV with anti-virals has significantly improved over the last several decades to the point that patients are living significantly longer and in "remission.". However, there is no cure yet. Former los angeles laker magic johnson is an example.