How should customer development look like after the product is launched?

I'll first answer this from a product and development perspective:
This answer is written assuming you have done everything right to launch a product that has already established product/market fit.

First, you want to fix the "leaky buckets." Brett Martin wrote a post-mortem of his startup and wrote: "Removing friction from existing user behaviors (e.g. checkins) almost always has a higher ROI than building castles in the sky (e.g. hypothesizing about your API). Find all the dead ends/local maxima in your current products before building new ones!" source: https://medium.com/p/72c6f8bec7df

Once you've done that, you'll be making prioritizing new features, metrics movers and customer delight. Adam Nash has a great post on product planning process here: http://blog.adamnash.com/2009/07/22/guide-to-product-planning-three-feature-buckets/

From a business perspective, your primary job is to be constantly talking to your actual users. As Brett explains in his post-mortem, one of the biggest mistakes entrepreneurs make is optimizing for people who aren't their customer. I believe strongly that the CEO of any startup should be heavily involved in customer support and, if the business is an enterprise business, in sales. There is just nothing as powerful as hearing from real customers.

Also, if you're selling anything, you want to be constantly tweaking the dials and experimenting with everything from pricing to conversion optimization.

And regardless of selling anything, conversion optimization is a daily activity, experimenting with new ways to fill the top of the funnel and bring them into the actions required to build your business.

Hope this helps. If you're asking because you're prepping for a launch or just launched, happy to do a call with you to provide more specific context.

You never really stop doing customer development. Remember that there are 5 main metrics for SaaS businesses: Acquisition, Activation, Retention, Revenue, and Referral. You might consider Customer Development as the process of validating hypothesis around how to drive those metrics.

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