How do i get to HKIA from Zhongshan port if my airline is not a partner airline?

Well, you can take a taxi to ZS Railway station and it takes about 15 minutes, around 30RMB. Then you can catch a bullet train to Gungzhou South within 30 minutes.

After that, take subway line 2 and then transfer to line 1 at Gongyuanqian, get off at Guangzhou East.

Take a train to HK and then take bus A21 to the airport.