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TVs are rather particular about flags. File formats (MP4, MKV) have flags. Matching them up is important.
By default, a lot of players will ignore subtitles in files if they do not have BOTH the "default" and "forced" flag set. Handbrake does not, by default, set the "forced" flag players are looking for... but it does have a "search for subtitles marked as FORCED" function.
Since you did not say what file type or subtitle type you are using, it is difficult to say how to set the "forced" flag.