The term deaf (with a lowercase d) is generally not used clinically. In lay usage it can mean various degrees of hearing loss from moderate (possibly even slight or mild) impairments through profound loss. Similarly eliminating deafness is not a well defined concept.
The auditory system is complex and hearing loss can be caused by damage to any part from the outer ear all the way up to the auditory cortex (https://en.wikipedia.org/wiki/Cortical_deafness).
Conductive hearing losses are generally caused by damage to the outer and middle ears and can often be eliminated through surgery or hearing aids.
Damage to the inner ear can be treated with hearing or bypassed with cochlear implants. Neither of these eliminate deafness, but can restore a significant amount of functional hearing. The auditory system is described as having thousands of channels while a cochlear implant has a dozen or so. Hearing aids simply turn up the volume so other channels can detect the sound, but there are still missing/damaged channels.
This is also research into hair cell regeneration that could repair some types of damage to the inner ear. While the research looks promising, it is technically difficult. You have to regrow the hair cell in the correct location with the right orientation and size. Then you need to stimulate nerve fibers to synapse on the regrown cell. you have to also worry about the supporting cells and the rest of the structures in the inner ear.
Damage to the auditory nerve can be bypassed with auditory brainstem implants and midbrain implants. These devices do not eliminate deafness, but do restore functional hearing. Again, the number of channels (and the processing the brain does on the sound) limit the performance of the device.