Both my DDs went from a good state primary school to Independent Senior school, as did quite a large number of their friends. They did a few practice papers beforehand, plus had about 2 months of weekly tuition sessions just to make sure they were comfortable. Both had the choice of 2 schools - one selective, one not. They are in Years 8 and 7, both doing well, and loving it.
It may depend on where you are, and the ethos of the school you're looking at. Have you gone along to one of the senior school open days, and asked them?
We will put DS into state infant school, but then are considering prep school rather than the state primary, but only because there seem to be much fewer options for boys at senior level than for girls, and the competition for places is likely to be much higher.