Check your local regs, but it is almost certain that you can be licenced. The attitude of an employer might have to be considered.
I think the ICAO standard permits up to 35dB loss in both ears, and greater loss in one ear is usually allowed subject to test. A typical test is having ATC read a message (IE a NOTAM)in the presence of an Examiner who assesses both the readablity of the message and the accuracy of the candidate.
Aircraft radios have more than enough gain to overcome any moderate deafness, but a greater problem will arise if there is not an adequate interphone system on the aircraft involved. Many operators persist in using ordinary speech across the cockpit, with radio supplied only through one headset earpiece, the other ear being left uncovered for crew speech. This gives a one-eared person a problem in trying to hear both conversation and radio, and requires careful juggling of the headset to half cover the good ear to achieve both functions. The effects will vary between left and right seats. However, none of this is insurmountable and I believe there are a number of professional pilots with little or no hearing in one ear.
If the aircraft is adequately equipped with interphone and an operator (enlightened, IMHO) uses headset for both intercom and radio, there is no problem whatever.