Synonyms of 'run after something or someone'
If you chase someone, or chase after them, you run after them or follow them quickly in order to catch or reach them.
She chased the thief for 100 yards.
If you follow someone who is going somewhere, you move along behind them without their knowledge, in order to catch them or find out where they are going.
I think we're being followed.
Thesaurus for run after something or someone from the Collins English Thesaurus