Most likely, and most.
With some media (magnetic type), this is not enough to completely obscure the recording … there may be traces "under" the new recording. You can not read that as usual, but with lab equipment, it's quite possible. This is why "erasing with a pattern" was invented (see Wikipedia about data persistence).
Even "erase with a pattern" will also be do not touch the blocks that in the meantime have been marked as "defective" (and replaced by supernumerary blocks) … they too could contain sensitive data, readable with lab equipment.
The actions to be taken depend largely on the thread scenario. If it is your private machine with holiday photos, crush will do the trick. If you have handled top secret data: shred, dissolve in an acid, use an angle grinder / drill or melt the drive with thermite could be the solution.