As of April 2021, this document from the UK states information about how healthcare professionals should look for and treat thrombosis and thrombocytopenia:
From the above document,
Cases usually present 5-28 days after vaccination and are characterised by thrombocytopenia, raised D Dimers
and progressive thrombosis, with a high preponderance of cerebral venous sinus thrombosis. Pulmonary
embolism and arterial ischaemia are also common. Bleeding can be significant and unexpected.
May 7, 2021, this was published in the United Kingdom: Guidance: Information for healthcare professionals on blood clotting following COVID-19 vaccination
From the above site:
Since March 2021, there have been reports from the UK and internationally of an extremely rare condition characterised by thromboembolic events (blood clots) accompanied by thrombocytopenia (low platelets) following the first dose of the AstraZeneca (AZ) COVID-19 vaccination. This includes cerebral venous sinus thromboses (CVST) where blood clots develop in the cerebral veins occurring together with low platelet counts. These cases are particularly unusual because despite low platelets, there is progressive thrombosis (formation of blood clots which block blood vessels).