This is exactly why patience is the first crucial factor. It is obvious that the cat will not take such a suggestion without some kind of argument. Anyway, if we are talking about an apartment cat, we can say it is important for it to get used to the idea that it is not imperative that once out of the house something bad is going to happen.
Use your imagination and first build a surrounded space for your cat. And don’t forget that the cat would be really happy to climb something. High plants or low trees can be an attraction to your cat.
Buy a collar for the cat and try to get her used to it. It is important that it would be worn just around the house at first. The same thing needs to be done with the leash. After a few days, encourage her by walking short distances on the leash, tempting her with a toy or some food. Then get out of the house for short walks. Increase distance one day at a time. Pick quiet places and make sure she got used to the outside street noise.
If you really want to make her walk on a leash, then try to get her with you when you are going shopping or on longer walks.
In time you can make her accept routes with intense traffic, but it is important for her to feel safe and to understand that she can rely on you. And if she wants to run around a little, make sure the collar isn’t too rigid.
You can even place a bell on her collar to find her easier in case she escapes or hides behind a bush. It will stop her from hunting, but take the bright side of this suggestion. You can find your cat even if somehow she runs away or escapes from the collar.