get up a thirst
and work up a thirstFig. to do something that will make one thirsty. (Fixed order.) Jogging makes me work up a thirst. Doing this kind of work always gets up a thirst with me.
have a thirst for something
1. Lit. to be thirsty for something to drink. I have a thirst for a tall glass of iced tea.
2. Fig. to have a craving or desire for something. The tyrant had an intense thirst for power. The actor's thirst for fame caused him to become unscrupulous.
thirst for something
1. Lit. to desire something to drink. (Somewhat formal.) "I thirst for something cooling and refreshing." said the preacher. You could see that everyone there was thirsting for water, or even coffee, but there was no refreshment in sight.
2. Fig. to have a strong desire for something. (See also
have a thirst for something.)
In the old days, students were said to thirst for knowledge. The generals thirsted for new battles to be fought.