To "develop a taste for" something means to begin to like how it tastes, after eating or drinking it several times. You especially use this phrase to talk about food or drinks that most people don't like at first. For example, a lot of people start out not liking things like:

• beer
• olives
• fermented foods
• vinegary foods
• spicy peppers

But after you eat them a few times, you start to like them. That's called "developing a taste for" them.

You can also "develop a taste for" things other than food, like a certain kind of artwork:

I'm starting to develop a taste for some of the Surrealist painters.