Neighbor from the upper floor has a leakage, the water is dripping through the ceiling...

How could a solicitor help? Are you living in an apartment block with a management committee?

If you're the owner of your unit, ring the property management company your OMC has hired to manage the building and advise them of the situation. If they also can't get ahold of the owner of the upstairs unit in question, they'll likely send out their own plumber to address the issue and stop the leak. Once the immediate issue is taken care of, you'll have to sort out the insurance with the block insurer and your own contents insurance policy, depending on who covers what and what excesses are involved. You might end up having to pay something out of pocket if the damage isn't covered by either policy or if there is an excess for water damage on both policies. If the cause of the water egress was your upstairs neighbour's negligence or deliberate actions (as opposed to some random plumbing failure that they couldn't reasonably have anticipated or prevented), you might have a legal case against them for any damages you suffered; that's when it might be time for a solicitor, if the costs you ended up having to pay were significant.

If you are renting the place, you'll need to contact your landlord, who will need to do all of the above (though if you can't get ahold of the landlord right away, go ahead and ring the property management company yourself to report it so they can take action as quickly as possible). Any damage to the unit or to the landlord's belongings inside the property (furniture, appliances, etc.) would be the landlord's responsibility to address. Any damage to your own belongings would need to be claimed on your own contents insurance; if you don't have contents insurance or your policy excludes this particular situation, then you'll likely have to pay out of pocket. You most likely would not have a claim against the landlord, the OMC, or your upstairs neighbour unless the leak was caused by negligence or deliberate actions on the part of one of those parties.

You apartment insurance company , but first the management company

it’s really bizarre your go straight to a solicitor

That's so true! In my case, the leak originated 2 floors above my apartment! But best to try to find contacts yourself... the MC might not be in a rush.