There is no direct connection from Annapolis Royal to Halifax. However, you can take the taxi to Middleton then take the bus to Halifax. Alternatively, you can drive from Annapolis Royal to Halifax in around 2 h 14 min.
From Annapolis Royal taxi to Middleton then bus to Halifax. 3 h 5 min $170. From Annapolis Royal drive to Halifax. 2 h 14 min $25. From Annapolis Royal drive to Digby, car ferry to Saint John, NB, drive to St John airport, fly to Halifax airport, then bus to Halifax. 6 h 52 min $455.