Cluster A phages can have tyrosine, serine integrases, or partitioning genes.
For the serine integrates, see the note about Bxb1 starts. Serine recombinases are called jumbo integrases because their size hovers around 500 amino acids (can go up over 700 amino acids). Look for serine residues in the N-terminus.
Historically we didn't differentiate serine integrases from tyrosine integrases. Ask for help if you can't tell which one is in your genome.
Some Cluster A phages, (I believe the first one identified is RedRock) don't have an integrase, but exist as an extra-chromosomal inhabitant of a bacterial cell. In order to be propagated, a partitioning system is utilized.

See this paper for details:
Dedrick RM, Mavrich TN, Ng WL, Cervantes Reyes JC, Olm MR, Rush RE, Jacobs-Sera D, Russell DA, Hatfull GF. Function, expression, specificity, diversity and incompatibility of actinobacteriophage parABS systems. Mol Microbiol. 2016 Aug;101(4):625-44. doi: 10.1111/mmi.13414. Epub 2016 Jun 10. PMID: 27146086; PMCID: PMC4998052.