"嗅着气味追赶" can be translated into English as "chase after by following the scent" or more naturally as "track down by following the smell".
Here are some example sentences:
The dog is chasing after the suspect by following the scent.
（那只狗正嗅着气味追赶嫌疑人。）
They tracked down the fugitive by following the smell he left behind.
（他们顺着他留下的气味追踪到了逃犯。）