How to effectively create list using if in java8?

I believe the cleanest way is as you have it. Nonetheless, you could use a helper method to avoid repeated if statements:

static void addIfPermitted(List<String> list, DeliveryAddressType addressType, 
    PermissionConstant permission) {

    if (SecurityUtils.getSubject().isPermitted(permission) {
        list.add(addressType.getValue());
    }
}

Now you can use this helper method this way:

List<String> deliveryAddressTypeList = new ArrayList<>(Arrays.asList(
    DeliveryAddressType.MY_DEFAULT_ADDRESS.getValue()));

addIfPermitted(deliveryAddressTypeList, 
    DeliveryAddressType.DEPOT_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_PFDEPORTS);

addIfPermitted(deliveryAddressTypeList, 
    DeliveryAddressType.CONTACT_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_ALL_CONTACTS);

addIfPermitted(deliveryAddressTypeList, 
    DeliveryAddressType.AN_ALTERNATIVE_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_FREE_FROM_ADDRESS);

If you want to use java 8 stuff, you could create a Map<DeliveryAddressType, PermissionConstant>:

List<String> deliveryAddressTypeList = new ArrayList<>(Arrays.asList(
    DeliveryAddressType.MY_DEFAULT_ADDRESS.getValue()));

Map<DeliveryAddressType, PermissionConstant> map = new HashMap<>();

map.put(DeliveryAddressType.DEPOT_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_PFDEPORTS);
map.put(DeliveryAddressType.CONTACT_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_ALL_CONTACTS);
map.put(DeliveryAddressType.AN_ALTERNATIVE_ADDRESS, 
    PermissionConstant.PHARMISA_DELIVERY_FREE_FROM_ADDRESS);

And then:

map.forEach((addressType, permission) -> 
    addIfPermitted(deliveryAddressList, adressType, permission));

Another way, using streams and the same map, but creating the final list from the map keys:

List<String> deliveryAddressTypeList = map.entrySet().stream()
    .filter(e -> SecurityUtils.getSubject().isPermitted(e.getValue()))
    .map(Map.Entry::getKey)
    .map(DeliveryAddressType::getValue)
    .collect(Collectors.toList());

deliveryAddressTypeList.add(DeliveryAddressType.MY_DEFAULT_ADDRESS.getValue());

Here you filter map entries and keep only the ones whose value (PermissionConsdtant) is permitted by the security. Then you transform each filtered entry into its key (DeliveryAddressType) and then transform each DeliveryAddressType into its value. Finally, you collect all these delivery address type values to a list.