If the HPV you once had is now laying dormant in your system, and your immune system has fought the virus off - then no you will not infect people. However the virus can return again, no matter how supresed the virus is, although that is rare after years of no symptoms.
Drs usually consider genital warts (low risk) to be dormant after 6-24 months of having no symptoms. For cell change in the cervix (high risk) you can spot