Expect the acquirer to review whatever it has to run as one company. In the 2024 Leader's Edge reporting, one acquirer described its goal as unifying back- and front-office operations and standardizing "accounting processes, workflows, employee compensation plans, contracts with carriers and desktop applications." Another said non-client-facing operations, including HR, IT, finance and accounting, legal, carrier contracts and licensing, are integrated "right away, with an emphasis on data and technology first in line."
For a vendor that points to five areas to ask about: the agency management system, carrier connections, accounting and payments, the desktop tools staff use daily, and security.
Security is where rules come in. New York's Department of Financial Services says in its cybersecurity FAQs that "merging with or acquiring another company very likely constitutes a material change" that would require reviewing and potentially updating a covered entity's risk assessment, with considerations that include "the integration of Information Systems". The same FAQs say a plan to move key business processes or data to a third-party service provider very likely counts too. The NAIC Insurance Data Security Model Law (#668) tells a licensee to adjust its security program for changing business arrangements "such as mergers and acquisitions" and to "exercise due diligence in selecting its Third-Party Service Provider". It is a model law, state versions differ, and it exempts licensees with fewer than 10 employees from the section that holds both duties.
This is context, not legal or compliance advice; check the rule's own text and your counsel. For what a fuller vendor security review looks like, see how carriers run vendor security reviews.