Hamlet gives Gertrude some specific advice-what is it?

The answer is:

in act 6, scene 4, it is made explicit the advice that Hamlet gives to Gertrude. He wants Gertrude to repent having married to her ex-husband's brother, who was deceased and did not stay with him (Hamlet's uncle) in the future.

Hamlet consider that if she does it so, that would be virtuous, and wise.

Hamlet asks Gertrude to repent for her action in marrying her dead husband's brother. But he specifically advises her not to sleep with Claudius anymore. He orders her to be virtuous and avoid him if she sees him again.

Though Claudius frames Hamlet as a mad person, he is actually healthy and sane. He also asks Gertrude to not reveal about his sanity to Claudius. Gertrude while meeting Claudius again says that Hamlet is mad and not healthy.