Truncate file that is opened in another procces

If I try truncate -s 0 log.log (:>log.log has same behavior) the displayd space on disk do become free but the size (ls -l) of file is still the same (tho du shows less). As far as I understand, it happens because the pointer is still "old". This behavior causes that I cannot use cat ... | grep ... command: CLI says that file is binary. So the only way is to use less or another commands. So, how do I truncate file, that is opened in write mode in another proccess and have correct file size after truncate? I need data in log.log to be truncated to another file, or just delete whole data in file without deleting the file itself