This idiom means – improvise, act without preparation, to let things go as they may, determined on the circumstances,according to the demand of the situation, to decide what to do as things happen, instead of planning in advance
This expression, which is mostly used in informal contexts, comes from the world of music. When a musician plays it by ear he attempts to play or reproduce a piece of music without looking at the music sheet. He plays the piece from memory, and uses his ears to determine if what he is playing is correct or not.
Example
Rather than adopting a new academic strategy, the principal decided to play it by ear
I don’t know what I will do when she will come in front of me. Let’s just play it by ear
Jane said that she has to play it by ear because she is not sure where to go tomorrow morning.
We can play it by ear and decide where to meet later.