In short, by having fewer or less serious risk factors than the other matching recipients currently on the transplant waiting list. Age is a risk factor that goes into the calculation, not a contraindication.
Age is not a contraindication to transplantation but increasing age is
an incremental risk factor and it is often associated with other
comorbidity; few UK patients have been transplanted above the age of
65 years. 1
What they're saying there is that with increased age comes increased risk of failure. This is because as we age we don't tolerate and recover from major surgeries as well, and we are also more likely to have other illnesses.
To take a hypothetical example, consider two patients:
Patient 1 is 70 years old, suffering from heart failure but has no other significant health issues such as diabetes, COPD, etc.
Patient 2 is 40 years old, suffering from the same type of heart failure but also has diabetes, hypertension and kidney disease.
There's a decent chance Patient 1 would be the selected recipient in this case because he probably has better odds of surviving the procedure, and possibly even better odds of living longer afterwards. But the reality is that there are almost never just two potential recipients so this is a contrived example. Patient 1 would most likely be in "competition" with a dozen other recipients, most of whom will be younger and therefore won't have the age risk factor working against them.
In summary, the older patient's best hope is that he or she is in excellent physical condition apart from the heart problems that landed them on the transplant list. The link I cited above describes many of the risks and contraindications that are taken into account in the UK, which are very similar to the factors considered in other countries.