The Trinity TESOL cert is one of the two internationally recognised TEFL qualifications (the other being the Cambridge CELTA) so yes, it's a good start.
If TEFL work is what you're after then it'll put you in a better position to get a job in language centres/tutorial schools in HK for sure.
Dizzydancer's right in theory re mainstream teaching, but in practice there are TESOL qualified teachers working in both local mainstream schools and local private schools (not the likes of ESF, HKIS, etc. but small, private, English medium schools). But you'll need some experience under your belt to get those kind of jobs.
And you can be a career TEFL teacher - alongside the people who do TEFL to travel, or do it because they've no other skills HK wants, or are here with working partners and want to do something to keep them occupied, there are career TEFLers and there is a definite professional development path you can follow if you choose.