The phrase "after hailing" is correct and usable in written English.
It can be used in contexts where someone is acknowledging or greeting someone or something before proceeding with another action.
Example: "After hailing a taxi, she quickly jumped in and gave the driver her destination."
Alternatives: "following the greeting" or "after acknowledging".
AFTER hailing a taxi in La Paz recently, your correspondent was intrigued to see that the car's centre console was in Japanese.
After hailing W. as "classy," Vice acted unclassy.
Could Germany countenance throwing Poland out if it said no, only a year or two after hailing the historic achievement of welcoming the Poles in?
But the Romania international defender is confident he can help the Scottish champions win more silverware, after hailing Rangers as one of the top clubs in Europe.
Charles reluctantly follows Katherine's wish, but after hailing a cab, and putting Katherine in it, decides to stay, "These are my old stamping grounds".
Chancellor Angela Merkel of Germany is having to defend the sale of the troubled carmaker Opel to a Canadian-Russian consortium, just days after hailing the deal.
A sought-after soloist hailed for her "remarkable intelligence, musicality, and sense of insight," Judith Ingolfsson will begin studio teaching at Peabody in the fall 2019 semester.
The Poznan UN climate change summit, a year before Copenhagen and a year into the credit crunch, saw minister after minister hailing the green revolution response to climate change as our economy's saviour.
President Konare decided to deliver his after-dinner remarks, hailing renewed Unites States attention to Africa, in French.
pic.twitter.com/ezBxVKAlze April 4, 2014 Sri Lanka Qualified for the 2014 ICC Twenty20 World Cup final after hail struck their semi-final against West Indies in Dhaka.
Still time for someone to explode in violent fury... 90+2 min: Braga send Hail Mary after Hail Mary - a rosary of Hail Marys, you might say - into the Porto box but Porto repel them well.
