Iran currently restrains its foreign policy because it fears US and Israeli retaliation. With nuclear weapons, Tehran will be emboldened by the confidence that it can engage in provocation and use its nuclear weapons to deter the worst forms of retaliation. A more aggressive Iran will increase its support to terrorists and engage in tougher coercive diplomacy.
Nuclear weapons in Tehran will cause global nuclear proliferation, as other states in the Middle East seek their own nuclear weapons in response, and as Iran provides uranium enrichment technology to US enemies. The global nonproliferation regime would be weakened.
A nuclear Iran could threaten nuclear war to stop developments contrary to its interests, giving the world a nuclear scare every few years. And given that the nuclear balance between Iran and its adversaries would be less stable than the one that held between the United States and the Soviet Union during the cold war, these future crises could very well spiral out of control resulting in a nuclear exchange between Iran and Israel or even Iran and the United States.