The phrase "big shoes to fill" typically refers to the concept of taking on a responsibility or a role that was previously held by someone who was highly successful or accomplished. In the context of your clue, it suggests that there are high expectations or standards set by a predecessor that someone else must now strive to meet or exceed. It can also refer to the challenge of living up to the achievements or reputation of someone who came before you.
Note: The provided meaning of the answer is for the latest New York Times crossword puzzle clue: High standards established by a predecessor … or what you are presented with in this puzzle?. Explanations are generated by AI and may be inaccurate.