RestClient is not propgating TraceID

So, if you don`t use any external dependencies for tracing, you should implement this logic by yourself. Just an simple example how to forward header with correlation information:
First, add interceptor to your RestClient

@Configuration
public class AppConfig {
    @Bean(name = "myLocalhostRestClient")
    public RestClient restClient() {
        return RestClient.builder()
            .baseUrl("http://localhost:8080")
            .requestInterceptor((request, body, execution) -> {
                var correlationId = MDC.get("X-Correlation-Id");
                request.getHeaders().add("X-Correlation-Id", correlationId);
                return execution.execute(request, body);
            })
            .build();
    }
}

Than you can use it like this:

@RestController
public class Controller {
    private final RestClient localhostRestClient;
    public Controller(RestClient localhostRestClient) {
        this.localhostRestClient = localhostRestClient;
    }
    @GetMapping
    public String hello(@RequestHeader(name = "X-Correlation-ID", required = false) String correlationId) {
        if (!StringUtils.hasText(correlationId)) {
            System.out.println("this is a first request in a chain. generate correlation header by myself");
            correlationId = UUID.randomUUID().toString();
        }
        MDC.put("X-Correlation-Id", correlationId);
        var greetingResponse = localhostRestClient.get()
            .uri("/greeting")
            .retrieve()
            .body(String.class);
        return "Hello " + greetingResponse.toString();
    }
    @GetMapping("/greeting")
    public String greeting(@RequestHeader(name = "X-Correlation-ID") String correlationId) {
        System.out.println("Recieved correlation ID: " + correlationId);
        return "Some random Person";
    }
}

Based on the spring doc, you have to define a @Bean for RestClient.Builder for auto instrument with java agent

@Bean
public RestClient.Builder restClientBuilder() {
    return RestClient.builder()
            .defaultRequest(new TraceInterceptor());
}