What is the safest way to travel from Tehran to North-Pakistan?

From Quetta, you can take a train which travels to Punjab province. From there, you will almost certainly need to pass through Islamabad/Rawalpindi, which is the transit point to the Northern Areas and Azad Kashmir.

The most dangerous parts of the country are northern Baluchistan, the North West Frontier Province and Sindh, but you will skip the worst by taking the train. In the past, you could actually take the northern road between Quetta and Islamabad, but I wouldn't try that these days.

To give you an idea of the security risk, people driving their own vehicles between the Iranian border and Punjab seem to get a police escort (at least from Quetta). As far as I know, the train is considered safe. Elsewhere, travel by bus is normal.

Zahedan on the Iranian side of the border also has a bad reputation, so you may want to pass through quickly.

I am local resident of Hunza living in Berlin. I think the best way is to get a local contact/guide who can travel with you from Quetta to Hunza.

I would prefer to hire a local to and take public transport to travel. Once you are in Gilgit, you can travel all alone anywhere, any time to Hunza. It is safe!