Searched the board fairly thoroughly, but haven't found the situation of former US citizens acquiring or retaining GE discussed here. Consider this scenario:

• Alice is a natural-born US citizen, resident in the Netherlands 10+ years, and has recently naturalized as a Dutch citizen (i.e. VWP-eligible, GE-eligible). When applying for naturalization, she acknowledged that she would be required to relinquish her other (US) citizenship. She is married to a natural-born US citizen and permanent Dutch resident, with dual Dutch/US citizen children.
  • No criminal or arrest record whatsoever, in any country.
  • She is a native US english speaker, educated in the US, with an SSN, US birth certificate, and US work history before moving to the Netherlands.
• Now that her naturalization is complete, Alice has recieved the expected letter from the Dutch authorities giving her 6 months to provide proof of loss of nationality to their satisfaction. If the process takes longer, she must provide copious documentation of the steps taken to relinquish her US citizenship, and a new estimated timeframe for aquiring the proof they demand - a consular Certificate of Loss of Nationality (CLN).
  • Outside of a few exceptional circumstances that don't apply here, the Dutch government requires new citizens to prove they have relinquished their former citizenship(s), and they mean it. (The kids fall under the exception, since they cannot consent.)
  • The Dutch authorities are very well informed about the (slow, expensive) process of acquiring a CLN, and will follow up relentlessly even if it takes a year or more.
  • They WILL revoke Alice's newly-acquired Dutch nationality (and with it, her right to remain in the country) if Alice ignores their demands for proof of loss of citizenship or fails to satisfy them that she has taken this obligation seriously.
• Alice has, throughout her residency outside the US, scrupulously complied with all IRS filing requirements and does not meet the asset or historical tax liability thresholds to be considered a "Covered Expatriate" subject to an exit tax.
• Alice plans to submit her request to the US consulate in Amsterdam for a certificate of loss of nationality on the grounds that she has commited an expatriating act defined under 8 U.S.C. § 1481(a)(1) with the intention of relinquishing their US nationality, namely obtaining naturalization in a foreign state as an adult.
  • Note that this is different than formal renunciation (8 U.S.C. § 1481(a)(5)). (Formal renunciation is a bad idea because of the Reed Amendment, which as written applies only to one who "officially renounces" US citizenship.)
• Alice might like to apply for Global Entry to ease future visits to the US, even though she no longer plans to live there. Her home, job, and family are all in the Netherlands.

The question is when should she apply?

• Now, before she has applied for loss of US nationality, and while she is still considered a citizen by the US state department?
  • She would of course disclose her NL citizenship with the application, and upon loss of US citizenship, promptly update DHS to this effect.
  • But will her GE be revoked once she's no longer a US citizen, even though NL citizens are eligible for GE?
• Soon after relinquishing her US nationality (i.e. exclusively as a Dutch citizen)?
  • She has no track record of travel to - or timely exit from - the US as a Dutch citizen.
  • Let's say that as a non-resident US citizen, she made trips of between one and four weeks, once or twice a year to the US.
• After building a travel history to the US under VWP with an ESTA?
• Never?
  • Because it will just be a waste of time and money; Alice is either literally not eligible under some regulation I haven't seen, or as a matter of policy she will be excluded.