No underlying conditions in the individuals who suffered from Thrombosis with Thrombocytopenia Syndrome (TTS) after AstraZeneca vaccination were found, and no underlying conditions contraindicate or pose a special precaution to AstraZeneca vaccination to date. Rare clotting problems like cerebral venous thrombosis are more common among pregnant or postpartum women. Other risk factors for such events include recently starting oral contraceptives, sepsis, cancer, and having an underlying condition that increases the tendency to form clots such as Factor V Leiden deficiency or lupus. However, none of these conditions is associated with thrombocytopenia; these conditions have not been identified as a risk factor for TTS, therefore none of them represents a contraindication for vaccination against COVID-19.
Update (March 2023): Rare cases of TTS following vaccination are a contraindication for subsequent vaccination with the same vaccine.