Neighbourhood plans must be in general conformity with the strategic priorities of the Local Plan.
The examination process for neighbourhood plans differs from the examination process for Local Plans. Neighbourhood Plans are tested against a series of “basic conditions” and further information can be accessed here: https://www.gov.uk/guidance/neighbourhood-planning--2#the-independent-examination.
There is nothing to prevent neighbourhood plans being developed in advance of an up-to-date Local Plan or at the same time and the Planning Practice Guidance sets out that authorities and neighbourhood groups should work closely together in such instances.
Further advice can be accessed here: