Of course you can still have sex! HIV is not a reason to give up sex. Safer sex offers your partner very effective protection from HIV infection.
Most importantly: condoms offer very good protection during vaginal or anal sex. You can find other information on safer sex here.
If a condom tears during sex, it is also possible to reduce the risk of infection to your partner using HIV medication. Several weeks' treatment can prevent HIV from taking hold in the body. In most cases, the person remains HIV-negative. This treatment is called post-exposure prophylaxis (PEP). Your partner should begin treatment as soon as possible after being exposed to HIV. You can find more information about PEP here.