A good tester should always be proactive in their approach to delivery, as part of their job they should willingly engage with analysts and developers and feel comfortable asking questions, chasing progress, attempting to resolve any blocked issues and focusing on delivery.
Whether working in Agile framework and trying to deliver a story or sprint commitment, or working in more Waterfall environment and focusing on deadlines, the emphasis should always be on a route to completion and having a proactive and at times pragmatic approach to achieve that.
In addition, a good tester will share methods, approaches and documentation across their team to aid improvement.
Finally, a tester needs to have the confidence to say no and push back if they are being pressured into letting someone go out the door without having confidence in it. or if they feel process is being circumnavigated without good reason.
All of the above are constantly preparing testers to improve aptitudes and soft skills that naturally lend themselves to managerial duties.
That includes the ability to ensure process is followed under pressure to deliver, ensuring only critical activities are followed to focus on that delivery, harbouring and developing a team ethos to improve individually and as a team, and being confident enough to go to senior management with news that may not always want to hear.
A good manager has to have excellent interpersonal skills, a proactive mindset, the ability to compromise and be pragmatic when the time arises, but equally be strong enough to have courage in their conviction when the situation requires. All of that is equally true of a successful tester, so at of the fundamental transferable skills are in place and just need applying differently.