We define a cluster as a group of homologous proteins that are found grouped together in at least two different genomes and which are more conserved than what is expected for the pair of genomes.

EvolClust predicts conserved gene clusters from pairwise genome comparisons and infers families of related clusters from multiple (all versus all) genome comparisons. You can check the paper describing the algorithm in the following publication.

Marina Marcet-Houben, Toni Gabaldón, EvolClust: automated inference of evolutionary conserved gene clusters in eukaryotes, Bioinformatics, Volume 36, Issue 4, 15 February 2020, Pages 1265–1266, https://doi.org/10.1093/bioinformatics/btz706

Furthermore, you can see a summary of the algorithm in here:
Github

To search for existing clusters in a proteome not included in evolclustDB we provide HMM profiles. Profiles are build for each protein family found in the cluster and are joined in a single file to simplify the search of the cluster in a proteome of interest. In order to perform the search you need to have a single proteome for a given species in fasta format. HMMsearch can then be used to obtain a table with the hits the profiles have in the proteome. Gene order information will then need to be used to extract potential clusters. A script is provided in the github repository of EvolClust to help with this search. In order for it to work the fasta header for the proteome has to contain information of the placement of the protein within the genome following the evolclust format (Species code +""+ number indicating a contig +""+ number indicating the protein in such a way that correlative numbers indicate proteins that are located next to each other. i.e. YEAST_002_00234). Then the script can be executed and this will first perform the HMMsearch step and then filter the results and supply a list of clusters (for additional details see here).