Can I make HTTP POST request from Thymeleaf table in Spring Boot application

you are using Links and I don't think that is possible, you would need to use a form where you can specify the method POST to be used.

In the example below im using a <button> instead of a <a> element, but it will work, the only thing you need to do is to style your button with CSS to look like your links

<form method="POST" th:action="@{/edit(personId=${person.personId})}">
    <button type="submit" name="submit" value="value" class="link-button">This is a link that sends a POST request</button>
</form> 

now in your code should look like this

<tr th:each="person : ${persons}">                
    <td th:text="${person.personId}"></td>
    <td th:text="${person.name}"></td>
    <td th:text="${person.address}"></td>
    <td th:text="${person.telephone}"></td>
    <td th:text="${person.email}"></td>
    <td>
        <form method="POST" th:action="@{/edit(personId=${person.personId})}">
            <button type="submit" name="submit" value="value" class="link-button">EDIT</button>
        </form> | 
        <form method="POST" th:action="@{/delete(personId=${person.personId})}">
            <button type="submit" name="submit" value="value" class="link-button">DELETE</button>
        </form>
    </td>
</tr>

EDIT

As you just shared you Java code, in the controller you are expecting the personId not as a PathVariable, but as a RequestParam, in that case your form should have that value...

edit your form and add the person id as follows.

<form method="POST" th:action="@{/edit}">
    <input type="hidden" name="personid" id="personId" th:value="${person.personId}" />
    <button type="submit" name="submit" value="value" class="link-button">This is a link that sends a POST request</button>
</form> 

Notice also I changed the action of the form to be just /edit, as its what your controller looks like

Does anyone know if Thymeleaf allow a POST request per row of a table? Or do I have to write a simple HTML form per row?

HTML doesn't support POST request with links and you have to use forms (as Rayweb_on explained). But Thymeleaf allows you to define custom tags which helps a lot :

<a th:href="@{/edit(personId=${person.personId})}" custom:linkMethod="post">Edit</a>

... which would generate following HTML (assuming jQuery is available) :

<a href="#" onclick="$('<form action=&quot;/edit/personId=123456&quot; method=&quot;post&quot;></form>').appendTo('body').submit(); return false;">Edit</a>

Custom tag definition (without error checking to keep it simple) :

/**
 * Custom attribute processor that allows to specify which method (get or post) is used on a standard link.
 */
public class LinkMethodAttrProcessor extends AbstractAttributeTagProcessor {

    private static final String ATTR_NAME = "linkMethod";
    private static final int PRECEDENCE = 10000;

    public LinkMethodAttrProcessor(final String dialectPrefix) {
        super(
                TemplateMode.HTML, // This processor will apply only to HTML mode
                dialectPrefix,     // Prefix to be applied to name for matching
                null,              // No tag name: match any tag name
                false,             // No prefix to be applied to tag name
                ATTR_NAME,         // Name of the attribute that will be matched
                true,              // Apply dialect prefix to attribute name
                PRECEDENCE,        // Precedence (inside dialect's own precedence)
                true);             // Remove the matched attribute afterwards
    }

    @Override
    protected void doProcess(final ITemplateContext context, final IProcessableElementTag tag,
                             final AttributeName attributeName, final String attributeValue,
                             final IElementTagStructureHandler structureHandler) {

        // get the method name (tag parameter)
        final IEngineConfiguration configuration = context.getConfiguration();
        final IStandardExpressionParser parser = StandardExpressions.getExpressionParser(configuration);
        final IStandardExpression expression = parser.parseExpression(context, attributeValue);
        final String method = (String) expression.execute(context);

        // add custom javascript to change link method
        final String link = tag.getAttribute("href").getValue();
        final String action = "$('<form action=&quot;" + link + "&quot; method=&quot;" + method + "&quot;></form>').appendTo('body').submit(); return false;";
        structureHandler.setAttribute("onclick", action);
        structureHandler.setAttribute("href", "#");
    }
}

See the Thymelead documentation for example of how this custom attribute needs to be registered.