Why STMZH Tamil font not supported?

Our local DTP operators use one Senthamizh Tamil font ­STMZH ttf fonts mostly. While LO supports Tamil beautifully and all other Tamil fonts are displayed properly, this STMZH font alone is displayed as symbols. In MS Word, Notepad, PagePlus, InDesign, Scribus etc I do not experience any difficulty. In LO alone this Tamil font is not displayed properly. Why? Will you correct it?

No, unless you file a proper bug report with description of the problem (preferably with screenshots) and a link to the font in question. This is a place for “How do I…”-type of questions, not a bug tracker.

this STMZH font alone is displayed as symbols.

I’m not sure what you mean under as symbols (well, any font displays symbols), but the fact that, as you write:

all other Tamil fonts are displayed properly

is, in my opinion, quite a clear indication that the problem is probably about the font, not about LibreOffice. Thus, consider reporting the issue both to Bugzilla (see Mike Kaganski’s comment) and to the font developers/maintainers.