The phrase "after second reading" is correct and usable in written English.
It can be used in contexts such as legislative processes, academic evaluations, or any situation where something is reviewed or assessed a second time.
Example: "The bill was approved after second reading, moving it closer to becoming law."
Alternatives: "following the second review" or "post second evaluation".
Immediately after second reading Hewart rose and began a speech that was "as violent an attack as has ever been made in the Lords".
Double reading of mammograms led to a 40% increase in the most relevant group of abnormal findings (4.3% after first reading to 7.4% after second reading).
We have achieved a great deal in these negotiations - more in fact than the Council wished to see - and it is the first time that the Council's stance has changed between the common position after second reading and the conciliation procedure, in the sense that for the first time the Council, having initially rejected Parliament's wishes, then nevertheless agreed to them unanimously.
What the European Parliament has achieved for European consumers in the Conciliation Committee after second reading, in terms of safety, transparency and reliability, as well as in respect of labelling, what we fought to secure - and I use the word 'fought' advisedly - is a great success.
After first reading the play last winter, theater executives moved quickly to produce the world premiere.
When he picked up the novel after first reading the script, Mr. Mendes recalled, it "just slayed me".
STUMBLING upon Henry James's "Portrait of a Lady" 20 years after first reading it, Wendy Lesser discovered that revisiting this book was a "dizzying" and "vertiginous" engagement with a younger self.
I did so after first reading The Selfish Gene, but I ruefully admit that, at the time, it defeated me and I am not sure I will try again.
Yet another talked about how, after first reading "David Copperfield," as a teen-ager, she opened it again when she was pregnant, and found that it was a different book.
