Should I sell off my POSB Invest Saver Nikko AM STI holdings and then buy them again via Tiger Brokers when the price drops?

I think you should look at your investment strategies as a whole and evaluate if you want STI ETF to be in the portfolio and what percentage.

Fees/Commission is one of the biggest concern for investors who are starting out.

RSP with DBS does have its benefit as a multiplier condition and should you need to sell it for emergency I guess is a much simpler process.

Imo, some things to consider:
1) Are you so good at stock analysis that you're confident that it will drop significantly in the near term? Many ppl are unable to time the market well and end up losing on potential gains (aka me!).

2) I don't think POSB Invest saver charges a custodian fee (go check if they do, cuz I've never been charged any), so if you're planning to hold STI for a long I don't see a need for you to switch to tiger. You'll have to incur a transaction fee when you buy at tiger.

3) From my experience selling off my G3B on investsaver, there was no selling fee (for some reason no fee, I was surprised). If you buy on tiger, you'll occur a buy fee and when you sell, you'll get a sell fee. So why would you want to waste money?

Just my 2cents worth. You do you.

Edit
4) Also if your g3b has a significant value, your "relationship" with the bank is better as you have a higher net worth managed by the bank.