Does the Paid-Up Capital stay locked in the bank account of the Company?

No, the paid-up capital can be taken out immediately, but the money can be spent only for the business needs of the company.

Suggested Readings

What is the minimum Authorised Capital for Incorporating a Singapore Company? How soon can I start using my company’s paid-up capital? What is the procedure for increasing paid-up capital at a later date? What will be my liabilities if I have a high paid-up capital?