A key question we should ask about Tristram and Iseult is why Arnold uses this medieval legend. Remember the beginning of the biography on Arnold: "How is a full and enjoyable life to be lived in a modern industrial society?"
As we saw in the Switzerland poems (see the NA), Arnold has serious doubt about the nature of love, about the tension between real and imagined love as well as love that cannot be realized in a world that is isolating, lonely, and full of despair. The Tristram legend offers Arnold a way of exploring these ideas since it captures them in a dramatic and haunting manner. Review the key lines about love in Part III of the poem (lines 112-42). Note that Arnold does not judge the lovers in this poem.
Chivalry is also important in the poem. It shows Tristram as being worthy of belonging to King Arthur's court. The chivlaric code would prevent Tristram from acting on his passion and love for Iseult, but the love philter counteracts this code. But it also possible to argue the poem exposes the limits of chivalry since Tristram and Iseult's love transcends the code of chivlary and morality of marriage convention. (Compare this to Scott's Ivanhoe.)
For Arnold, the past offers a commentary on the present. Think about what this specific commentary is.