First generation interventions to target aging are presently in clinical development, or available but not yet widely used. They include senolytic drugs, and a whole range of approaches to upregulate various stress response mechanisms and improve mitochondrial function, among other options. Second generation interventions are under investigation in the scientific community, but remain some years away from earnest clinical development for one reason or another. Most of the possible approaches to the wholesale, reliable replacement of cell populations, for example.
The best of plausible futures is the one in which the most effective of these first and second generation interventions (a) become widely used and (b) produce significant gains in the healthy human life span, of ten to twenty years or more. We'll know one way or another by 2040, and the signs of efficacy should be there earlier than that. I'd wager that we could know by the early 2030s as to whether or not senolytics have a strong effect on human life expectancy in old age, for example. A five year study would be long enough to determine an outcome, but it will take a few years from where we are now in order to get such a study launched. The research community is still waiting on the arrival of compelling human data - to match the great animal data - on suppression of inflammation and improvement of tissue function throughout the body resulting from senolytic treatment.
Cancer will be a consequence of this success. The declines of late life in our species evolved in large part to lower the risk of death by cancer, by reducing cellular activity in damaged environments, at the cost of a slower and more drawn out death by organ failure. Many of the early therapies targeting function in old age are essentially compensatory, dialing up stem cell function or tissue function despite damage, overriding the normal reactions of the body to raised levels of cell and tissue damage. Some therapies do aim to repair cell and tissue damage, and will produce much the same outcome in terms of increased function, but any given collection of treatments will not repair all of the damage. In particular, mutational nuclear DNA damage will be challenging to repair.
Cancer is a numbers game. How many cells, how much cellular activity, how much damage, how long a span of time. Cancer risk is a combination of factors: stochastic mutation in nuclear DNA, the spread of mutations into somatic mosaicism, the inflammatory environment of aged tissues, driven in large part by senescent cells, and the growing incapacity of the aged immune system. To the extent that therapies can address these factors, cancer rates will fall. Cancer is not going to vanish entirely any time soon, however, given the mutation issue. Cancer is an inevitability on any time frame that is long enough, living in a body with nuclear DNA that is damaged enough.
Thus we should all get used to the idea that our lifetime risk of cancer will be notably higher than that of our ancestors, and plan accordingly. Robust, reliable approaches to detecting and destroying cancer are a very necessary part of the panoply of rejuvenation therapies that will be produced over the next few decades. Very broad anti-cancer technologies, such as interference in telomere lengthening, that can be applied to all cancers, will be needed in order to make cost-effective, rapid progress towards the medical control of cancer.
Ultimately, cancer will not be feared by long-lived individuals with access to modern medical technology. A great deal of work remains to get to that point. Once there, however, the cancers that we will suffer - briefly, before they are dealt with efficiency and quickly - will be badges of honor, a mark of the degree to which we have fought back degenerative aging.