For this specific file name format, you should look for subtitles on these reliable databases:
The 720p.BluRay.x264 version is a standard high-definition encode, but because different release groups (like THORA , EbP , or CtrlHD ) might have slight variations in frame rates or intro sequences, "standard" subtitles found on general sites can often drift out of sync. Where to Download subtitle Tekkonkinkreet.2006.720p.BluRay.x264.[...
Finding the Right Fit: A Guide to Tekkonkinkreet (2006) Subtitles For this specific file name format, you should
If you download a subtitle and it’s a few seconds off, don't delete it! Most modern media players allow you to adjust timing on the fly: Subscene is known for having "retail" subtitle rips
Look for the "English" entry with the highest rating. Subscene is known for having "retail" subtitle rips which match BluRay timings perfectly.
A great alternative for anime-specific releases where fansubs might offer more cultural context than the official translation. How to Fix Sync Issues