The phrase "a second time round" is correct and usable in written English.
It can be used to refer to doing something again or repeating an action after it has already been done once.
Example: "After considering the feedback, I decided to submit my proposal a second time round."
Alternatives: "again" or "for a second time".
"It would be much harder a second time round to get it past the party.
The Democrats are determined to make it his downfall a second time round.
The instinct to make money a second time round, with a book that follows a roughly similar format to its predecessor, is as old as the hills.
Time Heist manages the neat trick of both being incredibly complex and rather a lot of fun; the circular nature of the mission makes much more sense a second time round.
I feel so lucky with my husband – not everyone would love their partner a second time round if they met them again from scratch years later, which is essentially what has happened to us.
Most people, like you or I, seek a variety of flavours, so we change our preference a second time round – a phenomenon called "sensory specific satiety".
It will seem less of a risk second time round.
By contrast, Turnbull had done OK on climate change as a previous leader of the Liberal party, so it was assumed he would do a lot better second time round.
Lancashire had a sniff again second time round, when the two all-rounders were back in harness with the lead just 201, but they, and some biffing once again from Liam Plunkett, raised the lead to 348.
England and Lancashire paceman James Anderson backed Moores to do a better job second time round if offered the post.
This kind of bubble-popping was brilliant fun in the Bust-a-Move and Puzzle Bobble games, and King has done a much better job second time round in translating it to modern touchscreens.
