on the trail of (someone or something)
Following, pursuing, or tracking someone or something. Police are on the trail of two armed men who held up a liquor store late last night. Our top detective is on the trail of the stolen goods, sir.
*on the trail (of someone or something)
and *on the track of someone or somethingseeking someone or something; about to find someone or something. (*Typically: be ~; get ~.) I'm on the trail of a new can opener that is supposed to be easier to use. I spent all morning on the track of a vendor who can meet our requirements.