It’s complicated.

On the one hand, chickenpox vaccination means that there will eventually be fewer elderly people who carry chickenpox virus in their nerves, who are susceptible to virus reactivating and causing shingles.

On the other hand, it’s possible that for today’s older adults (who are too old to have been vaccinated as children) who still carry the virus, they’re exposed to less chickenpox in the environment (because fewer children are infected) so they have less immune boosting and the virus may be better able to reactivate. And in fact there has been a gradual increase in shingles for many years now, in many countries; especially in people between 30-60, i.e. those who probably didn't get chicken pox vaccine as children and who aren't old enough to get the shingles vaccine.

On the third hand, there’s apparently something else that may be increasing shingles incidence, other than vaccination. The increasing frequency started before the childhood vaccine was available, and doesn't parallel vaccine usage in general; so while it's possible that's one cause, it's not likely to be the only cause. Other explanations are basically handwaving, "better identification", or "unknown risk factors".

>One theory is that childhood varicella zoster virus vaccination has decreased the circulation of wild-type varicella virus [19, 20]. Without this exposure, the general population receives less exogenous immune boosting against varicella, increasing the risk of virus reactivation [19, 20]. However, studies have shown that the incidence of HZ has been increasing in the United States since before varicella vaccination introduction and is similar in countries with and without varicella vaccination [7, 21, 22]. Enhanced awareness of HZ by patients and healthcare practitioners, increased surveillance, and improved electronic health record coding practices are other potential drivers of the increasing number of HZ cases among middle-aged adults.

--Herpes Zoster and Postherpetic Neuralgia: Changing Incidence Rates From 1994 to 2018 in the United States

Also see

• Modelling varicella vaccination – What does a lack of surge in herpes zoster incidence tell us about exogenous boosting?
• The impact of the varicella vaccination program on herpes zoster epidemiology in the United States: a review