Not necessarily. At least three different things contribute here:
1) your new partner may not have the genetics to make a particularly invasive placenta, or he may, but the odds of "not" are better
2) the uterine arteries are stretched out after a first pregnancy, so it's easier for a subsequent placenta to implant properly
3) as you've aged a bit, you may have progressed farther towards chronic hypertension or developed some sort of underlying condition that can predispose a pregnancy to go preeclamptic
The hard thing about PE research is that it's multifactorial and heterogeneous, two big words that pretty much mean there are lots of ways to get it. You can get it because you've got clotting problems, or because your family has a strong history of chronic hypertension and you're going to develop it later, or because the placenta doesn't implant properly because of the immune system, or because of a freak accident in which half the placenta abrupts because you fall down the stairs or something, or because this particular placenta decides to develop trisomy 13 in just some of the lobes...
This is just one of the possible factors.
One of the top researchers on this says it's like blindness research was 100 years ago, when they just knew people stopped being able to see. Macular degeneration and retinopathy of prematurity both cause blindness, but for completely different reasons. PE is much the same way.
Does that make any sense?