Improve results of a clustering
The very obvious tip I would say is that K-means is not the algorithm you use for clustering text data in general. The nature of text data is a bit more complicated than structured data on which K-means is one of basic but still working algorithms (of course it also depends on the way you model the text i.e. how you convert a text dataset to a of numbers). Let me propose two things with one hint:

Hint

Document Clustering is also referred to as Topic Modeling. So you really need to have a look at this as I assume you didn't yet (according to using k-means for this problem). Now we see two standard algorithms for topic modeling but I strongly recommend you to see other algorithms as well.

NMF

Non-negative Matrix Factorization is a well-known decomposition method for non-negative matrices like TF-IDF or other variants of Bag-of-Words. You can simply apply it to your problem using SKLearn.

LDA

or Latent Dirichlet Allocation (don't get confused by Linear Discriminant Analysis). This is a pretty standard algorithm for topic modeling and implementations can be found in SKLearn, Gensim, NLTK, Spacy and other NLP/ML libraries.

Hope it helped! Good Luck :)