Я не вижу, в чем проблема ..
String url = "http://localhost:8080/libraryBranches/libraryBranch/updateNumberOfCopies";
RestTemplate restTemplate = new RestTemplate();
HttpHeaders httpHeaders = new HttpHeaders();
httpHeaders.add(HttpHeaders.AUTHORIZATION, "urAccessToken");
UriComponentsBuilder builder = UriComponentsBuilder.fromUriString(url)
.queryParam("numberOfCopies", "")
.queryParam("bookId", "")
.queryParam("branchId", "");
HttpEntity httpEntity = new HttpEntity(httpHeaders);
restTemplate.exchange(builder.toUriString(), HttpMethod.PUT, httpEntity, LibraryBranch.class);