>Very active or suddenly active
>Rise quickly
>A sudden burst of energy
>Drinking (alcohol) heavily
>A winning streak
In short, this idiom can be used in many situations. It can refer to a burst or sudden rise to stock prices, for sports results, a sudden burst of activity (for these situations it seems to have positive connotations) and for heavy alcohol consumption.
Example
The price of gold has been on a tear recently.
‘Why is he drinking so much?’ ‘He had some bad news earlier and he’s been on a tear since then
Real Madrid have been on a tear this season.