Does primary insurance cover a crime policy?

The question is unclear as posed.

A "crime policy" is one that is intended to cover an organization for a stated range of risks and losses.

The term "primary policy" is generally used to descrive a basic, underlying layer of coverage of some type. Therefore, there can exist a "primary" layer of crime coverage, on top of which can be additional ("excess") coverage that raises the coverage limits and affords greater coverage.

Therefore, they are really two different things.