I'm not sure exactly what you mean by "remote push to talk", but one possibility is that you want a switch that is more convenient, such as a foot switch. In that case you would want to get such a switch, and make sure that it's wired to be normally open, rather than normally closed. (Foot switches often have a micro switch inside with three contacts. Depending on where the wires are soldered, such a micro switch can function either normally-open or normally-closed. So if such a switch is wired normally-closed, moving a wire can change it to be normally-open.) Rigging your radio to use a different switch is a matter of rewiring your microphone plug to use the external switch, or better yet, making an adapter between the microphone and the radio to ignore the microphone's PTT switch and use the external switch instead. Using an external adapter means that the microphone doesn't need to be modified.
Another possibility is that you want the radio to automatically start transmitting when you talk into the microphone. This is a feature called "VOX", which is built into many radios. If your radio has VOX, then all you need to do is to turn it on. If your radio doesn't include VOX then it would be possible, but not necessarily practical, to add it by buying a microphone that includes VOX, or by building a circuit to implement it.
If you do use VOX, you might consider using a noise-cancelling microphone, so that external noise doesn't trigger the VOX as much. Noise-cancelling microphones work by actually having more than one microphone; circuitry compares the signal from the microphones, and removes the part of the signal that is common to all the microphones. What signal is left must be from a sound that was emitted close to one of the microphones, which was hopefully your voice.
If you're talking about a true remote PTT, where someone else pushes a button that turns transmit on for your radio over a wireless connection, then that is technically possible but would be difficult to implement.