Yes, you should obtain a HealthCert if travelling and if required by airlines/foreign authorities overseas to show a digitally verifiable proof of test and/or vaccination.
All hardcopy vaccination cards/ slips issued in Singapore, as well as test and/or vaccination records found on mobile applications such as TraceTogether and HealthHub are not meant for use overseas where a secure and tamper-proof record of test and/or vaccination may be required by the country/region.
The endorsed PDT and Vaccination HealthCerts issued by Singapore’s Ministry of Health are designed to be easily shared by travellers to facilitate inspection and digital verification. However, you will still need to follow the requirements of your destination country.