What are the chances of us discovering a previously undiscovered element?

Rather than discovering a new element, it's more likely that we will create a new element. We have not observed all elements with an atomic number higher than 94 (i.e., with more protons in the nucleus than plutonium has) in nature and therefore have not discovered them, but rather, we have produced them.

The reason we haven't discovered these elements is that they have a short half-life, meaning they decay very quickly into other elements. For example, the last confirmed element with 188 protons in its nucleus (Oganesson) has a half-life of a thousandth of a second. So, in one second, half of the atoms decay into others a thousand times. So, in one second, it will undergo 2 to the power of 1000 decays to half (which is 1 followed by 300 zeros). Such Mendelevium (with 101 protons in its nucleus) has a half-life of almost 60 days, so after a year, 1/64 of the original amount will remain, and after 2 years, it will be only 1/4096.

For example, carbon-14 has a half-life of over 5,000 years, which is why we typically (originally) use it for dating living organism. But this method is only useful for determining ages up to approximately 50,000 years. In older measurements, for example, we use the potassium isotope K-40, which has a half-life of approximately 1 billion years.

If the question were, what is the chance of us creating an element that has not yet been discovered, I would say there is such a chance, and work is being done on the discovery of elements with 119 and 120 protons. But it's unlikely we could create an element with an arbitrary number of protons. If the nucleus were too large, several problems would arise. The nuclear forces wouldn't be able to hold the nucleus together even for a very short time and the nucleus's electron shell would likely collapse. According to our understanding of electron behavior based on quantum physics, electrons would have to move faster than the speed of light. Another limitation is that the larger the nucleus, the more it repels other nuclei/protons, which makes it impossible to increase the number of protons in that nucleus. Therefore, it is believed that the limit for the heaviest nucleus (and thus for new elements) is 125 protons.