A user will need management console access to manage all extensions to be able to do this but this will also give access to inbound rules and extension groups as well as all extensions settings. They can though manipulate contacts within the contacts list from a 3CX client or webclient, with the right given to the extension 'Can manage company phone book', found under the extensions settings > Rights tab within the management console. Then from a 3cx client they can check the box to 'add to company phonebook' when adding contacts and can also modify existing contacts from within the client directly. From their webclient Contacts section on the left of the page then clicking into Company they can add modify and delete contacts found in the company phonebook.