In a nutshell, yes, but this might not always be the case.
It all depends on the qualifications the employer is seeking. And since the vast majority of jobs require at least a high school diploma, it’s safe to say that you’re going to need your diploma in the vast majority of your job applications.
Before applying for a job, be sure to go through the requirements. If it needs a high school diploma, you have to provide it; otherwise, you won’t be considered for employment.
That being said, it’s possible for an employer to list a high school diploma as one of the requirements and still not ask to see it. For example, let’s say there’s a job opening that requires a master’s degree.
If you’re interested in the job, it’s clear you have a master’s degree. The employer also expects that only master’s degree holders will apply. Come interview day and you’re expected to produce copies of your credentials, it’s perfectly okay to produce just your master’s degree.
The employer knows that you can’t obtain a graduate or even undergraduate degree without having obtained a high school diploma, so they might not bother to ask you for your diploma. As long as your graduate credential is verifiable, you’re good to go.