Definition of run after phrasal verb from the Oxford Advanced American Dictionary

 

run after

 phrasal verb
phrasal verb
 
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Phrasal Verbs

run after somebody/something

 
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to run to try to catch someone or something synonym pursue

run after somebody

(informal)
 
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to try to have a romantic or sexual relationship with someone synonym pursue He's always running after younger women.
See the Oxford Advanced Learner's Dictionary entry: run after