Being a Class A Trainer means you can train other people to become Class A or Class A+ Spotters. Trainers, however, can NOT sign off any of these instructor ratings. The instructors you train will have to pass an official test supervised by an Examiner or Chief Examiner of the Organization, who will then sign them off.
To get a Class A Trainer rating, you have to competently run a Class A and Class A+ Spotter course under the supervision of a (Chief) Examiner who can then sign you off, if your teaching skills and spotting techniques are considered to be up to standard. Once rated, you will be able to run Class A and Class A+ Spotter courses independently.