Neither had heard nor heard is correct or wrong.
Which you prefer depends on the context - as with multiple questions on this site concerning tense.
Imagine that you hear the sound of gunshots. You might well confide to a friend:
I heard (that) they started training exercises......
But, if you wanted to point out subsequent information, you could say:
I had heard (that) they started training exercises.... but my father reminded me that hunters were shooting the wild boar in the valley.
That's to say that the past perfect tense (using had) is used to emphasise that one action in the past preceded another action in the past.
Frequently, native English speakers simply use one past tense after another instead of the past perfect. It's more a question of preference than correctness.