I know "anecdotal" is not "data" ...
... but I personally know one immunocompromised person who has been vaccinated (couple weeks ago) and he's still here.
Said person was the recipient of a heart transplant a few years ago, and is permanently on anti-rejection drugs due to this.
Anyone who participates in SOAR, or VRRA, knows Mike and Linda.
"Is there a risk", certainly; there is no human activity that is completely without risk. Risk can be managed and controlled, but not completely eliminated.
"Is the risk associated with vaccine side-effects greater or less than the risks associated with contracting covid-19 at this person's age and with this person's existing conditions including the immunocompromised situation itself"? Is a question for the family doctor, although for an older adult, the balance is almost certainly on the side of being vaccinated to control the risks associated with covid-19.
It is for this reason that if I were one year older, I would be seeking AstraZeneca vaccination today if not yesterday. Infection and death rates for the UK, which has been using approx 50% Pfizer and 50% AstraZeneca, are readily available.