Apparently not. According to CAA in Taiwan:

1. CI and BR have rights over other airlines on TPE-HKG v.v.
2. AE and CI have rights over other airlines on KHH-HKG v.v.

Unless neither of the three airlines apply those routes and use up the 4 daily (or 5 from summer), Transasia and Far Eastern Transport are stuck with other routes, and probably can't get RMQ-HKG v.v. either with AE already flying 4 daily charters.

Hong Kong Airlines will most likely be the firm entrant to the market in TPE and KHH as of now.