In the play hamlet, is it implied that Gertrude was having affairs with Claudius before King Hamlets Death?

No but Claudius had feelings for her, that is one of the reasons why he killed King Hamlet, the other being that he wanted the power that came with being a king. Gertrude never had an affair with Claudius I'm not sure {even though she married him} that she ever really did love him, and you can see that she is very upset when King Hamlet has died.