Looking at test as part of a bigger programme of change as your organisation moves from your current approach to a more agile way of working, there are some key success factors to consider. This is not a complete list but a few key considerations
Get buy-in from all key levels and stakeholders in the organisation. At the top, senior management commitment, middle management and project management, staff on projects including testers, etc. If there is resistance then change will be slow or will fail. Highlighting the benefits to influencers at the various levels will help address any fears and alleviate resistance. Agile is about cultural change to ensure lasting benefits. Agile is not just an IT/Software Dev change. It requires engagement from key stakeholders such as Product Management/Business stakeholders to realise the benefits. Effective communication from leaders as to how the change will affect the various roles will be affected each team member and what the benefits will be. It is through trust and support and removing doubt that fear and resistance disappear.
Allow cross functional teams scope to change their process within whatever boundaries and standards are appropriate for your context (this will be very different for example in a safety critical/heavily regulated environment compared to one with lower quality requirements with the ability to rapidly roll back a buggy release)
From a test point of view, think about a high-level test strategy that represents the best you can do now with agile testing, This should be concise (you’re your version of Marick’s Testing Quadrants is a good starting point and how to apply with an iterative/incremental lifecycle). It should then evolve over time as you mature and based on feedback from teams on what is working and what obstacles need addressing. It should act as a guide to the team on how to do approach testing in an incremental lifecycle with testing more integrated into the lifecycle from the start.
Central support for organisational infrastructure changes such as moving from functional silos to cross functional teams, associated role changes, training required, etc.
Coach the teams to help Developers and Testers operate as a single team removing traditional barriers. Encourage developer-tester pairing on user stories and approaches such as acceptance test driven development to reduce the risk of iterations becoming mini-waterfalls with testing squeezed at the end. Have testers participate in backlog refinement sessions to help prevent defects.
Central support for technical infrastructure changes such as setting up and evolving Continuous Integration and associated Test Automation. The latter ideally making use of the concepts in the Test Automation pyramid from Mike Cohn applied as appropriate to your context.
Apply inspect & adapt to the move to agile. In other wordsuse the regular feedback to ensure you are on the right track and adapt when obstacles arise.