This is a very good question.
There are some STDs that are not curable like herpes, these can be still transferred.
Anyways you have been treated for STD in the past, your last check-up was clean and you have the same partner who is also clean, so do not worry as you both might have the same problems if at all present and go for unprotected sex.
You may not give STD or Receive unless either of you have. Get the STD panel checked again for both of you.
Use condom preferably.
All the best. Wishing you good health.
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