Harry Bagley is Clive's bestest buddy in the whole wide world. In fact, Harry is also a hero to Clive, who sometimes wishes that he could be an explorer and go have cool adventures like Harry. From the beginning, Clive refers to Harry as being "brave as a lion" (1.1.79). The only problem is that Harry has a thing for Clive's wife and for Clive's young son, Edward.
In fact, Harry and Edward have already had a sexual experience together, though we're not sure what exactly they did. All we know is that whatever it was, Edward wants to do more of it, as he tells Harry, "Take it out now and let me see it" (1.2.267). The "it" is of course Harry's penis, but Harry knows better than to do this with a bunch of people around.
Harry also tells Clive's wife Betty that he loves her and that she's all he thinks about. He tells Betty, "I don't want to want you. Of course I want you" (1.1.395), but you've got to wonder how this goes with what Harry's been doing with Edward… or Joshua, for that matter. Let's not forget that at the end of Act 1, Scene 1, Harry asks Joshua, "Shall we go in the barn and f---? It's not an order" (1.1.406). Joshua agrees and the two of them walk off together.
Finally, Harry makes a move on Clive, too, and Clive decides that the only way to deal with Harry being gay is to get Harry married as soon as possible. And guess what? That's exactly what happens. Harry marries Clive's (lesbian) governess, Ellen, and the two of them presumably go on to live not-so-happily ever after.