I'd suggest calling NUH directly and asking for their list of private gynaes, then checking with your friends or asking in mum groups which ones they've seen for delivery or follow-ups. My friend went with Dr Tan at NUH and said she was very patient with all the first-time mum questions, but honestly it's quite personal which doctor you click with, so maybe start with a consultation or two before deciding.
Hey mummy! Just sharing that i heard Prof Mahesh Choolani and Dr Pradip Dashraath… or if not, you can also ask the clinic staff directly for recommendation :)