Learn English – Antonym to ‘Assign’

Reinstate is the most idiomatic term, in my opinion (for AE). It conveys both that access is being granted now and that it was revoked in the past.

There is no special term for the output of an operator analogous to the special term for an input (operand), at least not in common use.

Per the Wikipedia article on operators:

The values combined are called operands, arguments, or inputs, and the value produced is called the value, result, or output.