Stop all flights at once when the news reports of interesting new virus start to appear. Quarantine all those who have arrived already or recently arrived in empty hotel rooms at government expense.
Ban large events and gatherings of all kinds for a while. Told companies to make people work from home if possible. Schools stay open for the moment. Tell population to wear masks (this one might be a hard sell in a non mask wearing culture where the virus does not appear to be an imminent threat though).
Tell any manufacturing companies that are capable of producing masks and face shields to switch some of their production capacity over to these things--with the threat that failure to do so will mean that the government will have to impose harsh control measures which shut down or greatly inconvenience companies and hurt their profits. Let companies stamp their names on the PPE that they make and trumpet their production all over social media as a form of PR.
Test and trace. Quarantine any mild cases in empty hotel rooms at government expense. Severe cases go into hospital and are quarantined from other patients. They are NOT sent out into care homes.
If virus still appears to be spreading after this, close schools for a spell and intensify test and trace until the virus is suppressed. There should be no need for a lockdown as long as the number of cases is never allowed to get over a certain number and as long as "big ticket" spreaders have been closed (cancelling mass events and closing schools for a while etc.). Many of the most successful countries suppressed the virus without an actual lockdown.
Once virus is eradicated, join travel bubbles with other countries which have succeeded in largely or completely suppressing the virus (S Korea, HK, Singapore, NZ, Oz, Thailand, Vietnam and probably Japan and others in the very near future). Continue to control all arrivals--two days in quarantine, testing, temp checks.
With virus suppressed, life can largely return to normal apart from restrictions on large events like music concerts above certain size (since these provide too rapid a way for a single infection to fan out among a large number of people), and probably mild restrictions on schools and companies to reduce opportunities for any spread of the virus should a cluster break out. I would also mandate masks in all public indoor places (disabilities excepted), as it is a measure which slashes risk at minimal economic cost.