[on the track of] or [on the trail of] Hunting or […]

[on the trail of] See: [ON THE TRACK OF].

[on the trigger] See: [QUICK ON THE TRIGGER].

[on the up and up] {adj. phr.}, {informal} Honest; trustworthy; sincere. […]

[on the vine] See: [DIE ON THE VINE] or [WITHER ON […]

[on the wagon] {adv. phr.} Participating in an alcohol addiction program; […]

[on the wane and on the wax] {adv. phr.} Decreasing and […]

[on the warpath] {adj. phr.}, {informal} 1. Very angry. * /When […]

[on the watch] {adj. phr.} Alert; watchful. * /The customs inspector […]

[on the way] or [on one's way] {adv.} or {adj. phr.} […]