'To gain access to somebody' means to get/acquire the possibility or permission to contact/speak to someone. It is usually used with reference to someone who it is normally difficult to speak to (someone famous or important) or in a situation (such as in prison) where contact is normally not permitted. 'The lawyer was not able to gain access to his client because the man had been put in solitary confinement.' We can also use gain access to a place ( which normally requires permission to enter) / to information (which is normally hidden or protected) 'Hackers gained access to the email addresses of customers of several large US banks.'

isnt it always a big problem my love ...

Gaining access to someone in the Computer world means also to hack their accounts or passwords.That is a specific meaning beside the general one Eliot mentioned.

Yes, you can. You can try to gain access to the president of the US, but that can be quite hard. It means: establish a direct communication with someone.