There have been cases of blood clotting, severe enough that in some places it is recommended that people under 40 get a different shot.

https://www.nhs.uk/conditions/coronavirus-covid-19/coronavir...

Here's the Australian Technical Advisory Group on Immunisation post from when Australia discontinued AstraZeneca for people aged under 60 (and made Pfizer the preferred vaccine instead):

https://www.health.gov.au/news/atagi-statement-on-revised-re...

From early April to 16 June 2021, 60 cases of confirmed or probable TTS [thrombosis and thrombocytopenia syndrome] have been reported in Australia. This includes an additional seven cases reported in the past week in people between 50-59 years, increasing the rate in this age group from 1.9 to 2.7 per 100,000 AstraZeneca vaccine doses.... TTS is a serious condition in a proportion of individuals who develop it. The overall case fatality rate in Australia (3%; 2 deaths among 60 cases) is lower than has been reported internationally.

At that time, more people were dying from AstraZeneca than were dying from Covid in Australia. During May & June 2021, no one died of Covid in Australia: https://www.abs.gov.au/articles/covid-19-mortality-australia...