I am on a Welsh Council. Our equivalent to NALC is One Voice Wales. They only allow the Clerk and the Chair of the Council to speak to them directly. Councillors are supposed to go via the Clerk. I can understand this up to a point. Some Councillors (especially new ones) may have questions that could easily be answered by the Clerk. If not, the clerk should find out for you. If OVW or NALC allowed every single Councillor to contact them they would possibly be overwhelmed with calls and emails. However, they do allow access to the members section on their website to all councillors. And this section can be very useful.
Our Clerk kept this information very quiet but when I found I asked for the login details and they where given to me. I am now the Chair and encourage other Councillors to explore the site. So, yes you most definitely should have access to the NALC website even if you can't phone them.
If you are having no joy with the Clerk than speak to the Chair. If he/she is doing their job properly they should be able to assist you by informing the Clerk that all councillors should have access to the NALC website.