The short answer
In countries and states with direct access, yes, and your website should say so on the first screen, because most patients still assume a dentist has to send them. Where a referral or a recent examination is required, the booking flow collects it up front so nobody arrives for a visit that cannot go ahead.
Which of those two you are is a question for your regulator, not for a web page. Everything below is what to do with the answer once you have it.
Why this is the most important line on the site
Direct access is the thing that makes an independent hygiene clinic possible, and it is the thing patients do not know exists. They have only ever been sent to a hygienist by their dentist. Left to their own assumptions, they will not book with you, and they will not ring to ask either.
That makes one sentence near the top of the home page worth more than any other content on the site. No referral needed, book online, with a button next to it.
Confirm the position with your regulator
Direct access and scope of practice vary a great deal.
In the United Kingdom the General Dental Council sets what registered hygienists and therapists may do and on what terms. In the United States it varies state by state, with each state dental board as the authority, and the arrangements differ in what supervision, prior examination or collaborative agreement they require. In Australia the Dental Board of Australia, through Ahpra, sets the terms. In Canada it varies by province.
Ask your own regulator what applies to you, ideally in writing, and keep the answer where you can find it when you next update the site. This is orientation rather than legal advice, and a website should never be the reason a clinic gets its scope wrong.
Where the message goes
The first screen of the home page. One sentence, plain words, a booking button beside it.
The price list. This is where the decision actually happens, so the referral position belongs there too.
The what-happens page. In its opening paragraph, before anything about the appointment itself.
The booking flow. Repeated at the point of booking, because that is where the doubt returns.
Four places, the same words in each. Rewriting it differently in each place is how a clinic ends up with two versions of its own position on the site.
If a referral or an examination is required
Do not hide it and do not bury it in small print. Say what is needed, say how a patient gets it, and collect it in the booking flow rather than at the door.
Practically that means a required field or upload at booking, a line in the confirmation message saying what to bring, and a short explanation of what happens if they arrive without it. A wasted appointment costs you the slot and costs the patient a morning, and both are avoidable with one field.
If you work with local dentists who refer to you, say so and name the practical route. Patients find that reassuring rather than restrictive.
What never to write
Do not use the phrase direct access as if it were a qualification or an approval you hold. Do not imply that you can do anything a dentist can do. Do not describe a treatment as suitable for a reader, because that is a clinical judgement that needs an assessment.
State the practical fact, which is whether a patient may book with you and what they need to bring, and leave everything clinical to the appointment.
Keep it editable
Regulatory positions change, and so do the arrangements a clinic works under. Build this line as an editable field rather than text baked into a template, so it takes two minutes to update in all four places when something changes, and put a yearly reminder in the calendar to check it is still correct.
Where this sits
Direct-access messaging on the first screen, repeated on the price list and inside the booking flow, is the first of the things every hygiene clinic website we build carries, and the same regulator-aware pattern runs through our dental practice websites. Packages are on pricing. Say the thing patients do not know, in the place they will read it, and the bookings follow.